Instabilities in Hydrodynamics

Modeling, analysis and numerics

Publications of the members of the team

  1. C. Lacave and N. Masmoudi, Impermeability through a perforated domain for the incompressible 2D Euler equations, submitted (Arxiv link).
  2. S. Angelopoulos, D. Arsenio and C. Durr, Infinite linear programming and the online search problem with turn cost, submitted (2014).
  3. C. Chalons, M. Girardin, S. Kokh, An all-regime Lagrange-Projection like scheme for the gas dynamics equations on unstructured meshes, submitted (Hal link)
  4. M. Strani and B. Texier, Time-delayed instabilities in complex Burgers equations, submitted (ArXiv link).
  5. F. Colombini, D. Del Santo, F. Fanelli and G. Métivier, The well-posedness issue in Sobolev spaces for hyperbolic systems with Zygmund-type coefficients, submitted (ArXiv link).
  6. D. Arsenio, S. Ibrahim and N. Masmoudi, A derivation of the magnetohydrodynamic system from Navier-Stokes-Maxwell systems, submitted (2014).
  7. C. Berthon, C. Chalons, A full well-balanced, positive and entropy-satisfying Godunov-type method for the shallow-water equations, submitted (Hal link)
  8. D. Gerard-Varet, D. Han-Kwan and F. Rousset, Quasineutral limit of the Euler-Poisson system for ions in a domain with boundaries II, submitted (Arxiv link).
  9. F. Fanelli and X. Liao, Analysis of an inviscid zero-Mach number system in endpoint Besov spaces for finite energy initial data, submitted (ArXiv link).
  10. M. Boileau, C. Chalons, M. Massot, Robust numerical coupling of pressure and pressureless gas dynamics equations for Eulerian spray DNS and LES, submitted (Hal link)
  11. F. Fanelli and X. Liao, The well-posedness issue for an inviscid zero-Mach number system in general Besov spaces, submitted (ArXiv link).
  12. E. Audusse, C. Chalons, P. Ung, A very simple well-balanced positive and entropy-satisfying scheme for the shallow-water equations, submitted (in revised form) in Commun. in Math. Sci., short version to appear in Proceedings in Mathematics and Statistics, Vol. 78, Jürgen Fuhrmann et al: Finite Volumes for Complex Applications FVCA7
  13. L. Oruba, E. Dormy Predictive scaling laws for spherical rotating dynamos, Geophys. J. Int., 198, 828–847, 2014 doi: 10.1093/gji/ggu159
  14. B. Texier, Approximations of pseudo-differential flows, submitted (ArXiv link).
  15. O. Glass, A. Munnier and F. Sueur, Dynamics of a point vortex as limits of a shrinking solid in an irrotational fluid, submitted (Arxiv link).
  16. D. Gerard-Varet and C. Lacave, The two-dimensional Euler equations on singular exterior domains, submitted (Arxiv link).
  17. M.-O. Bristeau, A. Mangeney, J. Sainte-Marie, N. Seguin, An energy-consistent depth-averaged Euler system: derivation and properties, submitted.
  18. C. Chalons, M. Massot, A. Vié, On the Eulerian large eddy simulation of disperse phase flows: an asymptotic-preserving scheme for small stokes number flows, submitted (Hal link)
  19. H. Bahouri, J.-Y. Chemin and I. Gallagher, Stability by rescaled weak convergence for the Navier-Stokes equation, submitted (Arxiv link).
  20. D. Gerard-Varet and L. Giraldi, Rough wall effect on micro-swimmers, submitted (Arxiv link).
  21. C. Cances, F. Coquel, E. Godlewski, H. Mathis, N. Seguin, Error analysis of a dynamic model adaptation procedure for nonlinear hyperbolic equations, submitted.
  22. D. Iftimie, G. Karch and C. Lacave, Asymptotics of solutions to the Navier-Stokes system in exterior domains, submitted (Arxiv link).
  23. M. Ndjinga, T.-P.-K. Nguyen, C. Chalons, Numerical simulation of an incompressible two-fluid model, Proceedings in Mathematics and Statistics, Vol. 78, Jürgen Fuhrmann et al: Finite Volumes for Complex Applications FVCA7
  24. Y. Lu and B. Texier, A stability criterion for high-frequency oscillations, submitted (ArXiv link).
  25. C. Lacave, E. Miot and C. Wang, Uniqueness for the 2-D Euler equations on domains with corners, to appear in Indiana Univ. Math. J. (Arxiv link).
  26. V. Bonnaillie-Noel, C. Lacave and N. Masmoudi, Permeability through a perforated domain for the incompressible 2D Euler equations, to appear in Ann. Inst. H. Poincare Anal. Non Lineaire (Arxiv link).
  27. M. Tournus, N. Seguin, B. Perthame, S. Randall Thomas, A. Edwards, A Model of calcium transport along the rat nephron, American Journal of Physiology - Renal Physiology, volume 305(7), pages F979--F994, 2013.
  28. D. Arsenio and L. Saint-Raymond, Solutions of the Vlasov-Maxwell-Boltzmann system with long-range interactions, C. R. Math. Acad. Sci. Paris 351(9-10), 357-360 (2013).
  29. R. Bürger, C. Chalons, L.-M. Villada, Anti-diffusive and random-sampling lagrangian-remap schemes for the multi-class Lighthill-Whitham-Richards traffic model. SIAM J. Sci. Comput. 35-6, pp. B1341-B1368 (2013)
  30. C. Lacave, T. Nguyen and B. Pausader, Topography influence on the Lake equations in bounded domains, J. Math. Fluid Mech., Volume 16, Issue 2 (2014), pp. 375-406 (Arxiv link).
  31. B. Texier and K. Zumbrun, Entropy criteria and stability of extreme shocks: a remark on a paper of Leger and Vasseur, to appear in Proc. Amer. Math. Soc. (ArXiv link).
  32. Th. Bodineau, I. Gallagher and L. Saint Raymond, The Brownian motion as the limit of a deterministic system of hard-spheres, in revision at Inventiones Mathematicae (Arxiv link).
  33. M. Tournus, A. Edwards, N. Seguin, B. Perthame, Analysis of a simplified model of the urine concentration mechanism, Networks and Heterogeneous Media, vol.7(4), 2012.
  34. A. Ambroso, C. Chalons, F. Coquel, T. Galié, Interface model coupling via prescribed local flux balance, Mathematical Modelling and Numerical Analysis, Vol. 48(3), pp 895-918 (2014)
  35. D. Gerard-Varet and N. Masmoudi, Well-posedness for the Prandtl system without analyticity or monotonicity, submitted (Arxiv link).
  36. C. Cancès, H. Mathis and N. Seguin, Relative entropy for the finite volume approximation of strong solutions to systems of conservation laws, submitted (HAL link).
  37. B. Andreianov, F. Lagoutière, N. Seguin and T. Takahashi, Well-posedness for a one-dimensional fluid-particle interaction model, SIAM Journal on Mathematical Analysis, volume 46(2), pages 1030-1052, 2014. (HAL link).
  38. A.L. Dalibard and C. Prange, Well-posedness of the Stokes-Coriolis system in the half-space over a rough surface, submitted (ArXiv link).
  39. F. Coquel, J.-M. Hérard, K. Saleh and N. Seguin, A robust entropy-satisfying finite volume scheme for the isentropic Baer-Nunziato model, Mathematical Modelling and Numerical Analysis (M2AN), volume 48, pages 165--206, 2013. (HAL link).
  40. C. Berthon and C. Chalons, A full well-balanced, positive and entropy-satisfying Godunov-type method for the shallow-water equations, submitted.
  41. D. Gerard-Varet, M. Hillairet and C. Wang The influence of boundary conditions on the contact problem in a 3D Navier-Stokes flow, to appear in J. Math. Pures App. (Arxiv link).
  42. F. Coquel, K. Saleh and N. Seguin, A robust and entropy-satisfying numerical scheme for fluid flows in discontinuous nozzles, Mathematical Models and Methods in Applied Sciences (M3AS) (HAL link).
  43. C. Chalons, M. Girardin and S. Kokh, Large time-step and asymptotic-preserving numerical schemes for the gas dynamics equations with source terms, SIAM J. Sci. Comput. 35-6, pp. A2874-A2902 (2013).
  44. S. Ervedoza, M. Hillairet and C. Lacave, Long-time behavior for the two-dimensional motion of a disk in a viscous fluid, Comm. Math. Phys., Volume 329, Issue 1 (2014), pp. 325-382 (Arxiv link).
  45. M. Bonnivard, A.L. Dalibard and D. Gerard-Varet, Computation of the effective slip of rough hydrophobic surfaces via homogenization, to appear in M3AS (Arxiv link).
  46. H. Mathis, C. Cancès, E. Godlewski and N. Seguin, Model adaptation for hyperbolic systems with relaxation, submitted (HAL link).
  47. C. Chalons, M. Girardin and S. Kokh, Operator-splitting based AP schemes for the 1D and 2D gas dynamics equations with stiff sources, Proceedings of the 2012 International Conference on Hyperbolic Problems: Theory, Numerics, Applications.
  48. I. Gallagher, L. Saint Raymond and B. Texier, From Newton to Boltzmann: hard spheres and short-range potentials, Zurich Lectures in Advanced Mathematics 18 (2014), 148 pages (Arxiv link).
  49. C. Chalons, P. Engel and C. Rohde, Convergence proof for a conservative scheme for hyperbolic-elliptic phase transitions problems, SIAM J. Numer. Anal., 52(1), 554–579 (2014).
  50. M. Hillairet and P. Wittwer, On the existence of solutions to the planar exterior Navier Stokes system, to appear in Journ. Diff. Equ. (Arxiv link).
  51. D. Gerard-Varet and M. Hillairet, Existence of weak solutions up to collision for viscous fluid-solid systems with slip, Comm. Pure Appl. Math., to appear (Arxiv link).
  52. M. Schrinner, L. Petitdemange, R. Raynaud, E. Dormy Topology and field strength in spherical, anelastic dynamo simulations A&A 564, A78, 2014 DOI: 10.1051/0004-6361/201322801
  53. D. Arsénio and N. Masmoudi, A new approach to velocity averaging lemmas in Besov spaces, J. Math. Pures Appl. (9) {\bf 101}(4), 495-551 (2014) (Arxiv link).
  54. J.-Y. Chemin, I. Gallagher and C. Mullaert, The role of spectral anisotropy in the resolution of the three-dimensional Navier-Stokes equations, Studies in Phase Space Analysis with Applications to PDEs, Progress in Nonlinear Differential Equations and Their Applications 84, Birkhauser, pages 53-79, 2013 (Arxiv link).
  55. A.L. Dalibard and L. Saint-Raymond, Mathematical study of degenerate boundary layers, submitted (ArXiv link).
  56. F. Coquel, J.-M. Hérard, K. Saleh and N. Seguin, Two properties of two-velocity two-pressure models for two-phase flows, to appear in Communications in Mathematical Sciences (HAL link).
  57. A.L. Dalibard and D. Gerard-Varet , On shape optimization problems involving the fractional laplacian, ESAIM COCV vol. 19, Issue 14, pp 976-1013 (2013) (Arxiv link).
  58. P. Mishra, C. Gissinger, E. Dormy, Stephan Fauve, Energy transfers during dynamo reversals EPL (Europhysics Letters), 104, 69002, 2013. doi:10.1209/0295-5075/104/69002
  59. C. Lacave, 3D Viscous Incompressible Fluid around One Thin Obstacle, to appear in Proc. Amer. Math. Soc. (Arxiv link).
  60. A. Moussa and F. Sueur, A 2d spray model with gyroscopic effects, Asymptotic analysis, Volume 81, Issue 1, 53-91, 2013 (Arxiv link).
  61. F. Sueur, On the motion of a rigid body in a two-dimensional ideal flow with vortex sheet initial data, Annales de l'Institut Henri Poincare (C) Non Linear Analysis Volume 30, Issue 3, May–June 2013, Pages 401–417 (Arxiv link).
  62. D. Gerard-Varet , D. Han-Kwan and F. Rousset, Quasineutral limit of the Euler-Poisson system for ions in a domain with boundaries, Indiana Univ. Math. Journal, to appear (Arxiv link).
  63. F. Sueur, A Kato type Theorem for the inviscid limit of the Navier-Stokes equations with a moving rigid body, Comm. Math. Phys. December 2012, Volume 316, Issue 3, pp 783-808 (Arxiv link).
  64. I. Gallagher and H. Bahouri, Weak stability of global solutions to the incompressible Navier-Stokes equations, Arch. Ration. Mech. Anal. 209 (2013), no. 2, 569–629 (Arxiv link).
  65. L. Petitdemange, E. Dormy, S. Balbus, Axisymmetric and non-axisymmetric Magnetostrophic MRI modes Physics of the Earth and Planetary Interiors, 223, 21-31, 2013. doi:10.1016/j.pepi.2013.03.003
  66. C. Lacave, Uniqueness for two dimensional incompressible ideal flow on singular domains, submitted (Arxiv link).
  67. F. Sueur and T. Nguyen, Boundary layers interactions in the plane parallel incompressible flows, Nonlinearity, Volume 25, Issue 12, p3327-3342, 2012 (Arxiv link).
  68. D. Gérard-Varet and C. Lacave, The 2D Euler equation on singular domains, Arch. Ration. Mech. Anal., Volume 209, Issue 1 (2013), pp. 131-170 (Arxiv link).
  69. D. Iftimie, G. Karch and C. Lacave, Self-similar asymptotics of solutions to the Navier-Stokes system in two dimensional exterior domain, unpublished (Arxiv link).
  70. O. Glass and F. Sueur, On the motion of a rigid body in a two-dimensional irregular ideal flow, SIAM Journal on Mathematical Analysis. Volume 44, Issue 5, 3101-3126 (Arxiv link).
  71. I. Bouya, E. Dormy Revisiting the ABC flow dynamo Physics of Fluids 25, 037103, 2013 doi:10.1063/1.4795546
  72. C. Chalons, F. Coquel, Modified Suliciu relaxation system and exact resolution of isolated shock waves, M3AS, Vol. 24, No. 5 937–971 (2014).
  73. O. Glass, C. Lacave and F. Sueur, On the motion of a small body immersed in a two dimensional incompressible perfect fluid, to appear in Bull. de la SMF (Arxiv link).
  74. E. Audusse, C. Chalons, O. Delestre, N. Goutal, M. Jodeau, J. Sainte-Marie, J. Giesselmann and G. Sadaka, Sediment transport modelling : relaxation schemes for Saint-Venant-Exner and three layer models, ESAIM Proceedings Cemracs, vol 38, pp 78-98 (2012).
  75. C. Cancès and N. Seguin, Error estimate for Godunov approximation of locally constrained conservation laws, SIAM Journal on Numerical Analysis (SINUM), volume 50(6), pages 3036-3060, 2012.
  76. C. Chalons, P. Goatin and N. Seguin, General constrained conservation laws. Application to pedestrian flow modeling, Interfaces and Free Boundaries, vol 8(2), pp 433-463 (2013).
  77. E. Feireisl, I. Gallagher, D. Gérard-Varet and A. Novotny, Multi-scale analysis of compressible viscous and rotating fluids, Comm. Math. Phys. 314 (2012), no. 3, 641–670 (Arxiv link).
  78. G. Métivier, B. Texier and K. Zumbrun, Existence of quasilinear relaxation shock profiles, Ann. Fac. Sci. Toulouse Math. (6) 21 (2012), 1, 1--23.
  79. B. Andreianov and N. Seguin, Analysis of a Burgers equation with singular resonant source term and convergence of well-balanced schemes, Discrete and Continuous Dynamical Systems - Series A (DCDS-A), volume 32(6), pages 1939-1964, 2012.
  80. C. Berthon, C. Chalons and R. Turpault, Asymptotic-preserving Godunov-type numerical schemes for hyperbolic systems with stiff and non-stiff relaxation terms, Numerical Methods for Partial Differential Equations (NMPDE) vol 29(4), pp 1149-1172 (2013).
  81. D. Gerard-Varet and M. Hillairet, Computation of the drag force on a rough sphere close to a wall, M2AN, vol. 46, Issue 05, pp 1201-1224 (2012) (Arxiv link).
  82. M.-D. Thanh, D. Kröner and C. Chalons, A robust numerical method for approximating solutions of a model of two-phase flows and its properties, Applied Mathematics and Computation, vol 219, pp 320-344 (2012).
  83. M. Schrinner, L. Petitdemange, E. Dormy Dipole collapse and dynamo waves in global direct numerical simulations Astrophysical Journal (ApJ) 752, 121, 2012 doi:10.1088/0004-637X/752/2/121
  84. C. Lacave, Two Dimensional Incompressible Ideal Flow Around a Small Curve, Commun. in Part. Diff. Eq., 37:4 (2012), 690-731 (Arxiv link).
  85. O. Glass and F. Sueur, The movement of a solid in an incompressible perfect fluid as a geodesic flow, Proc. of the AMS, Volume 140, No.6, p2155-2168, 2012 (Arxiv link).
  86. C. Chalons, D. Kah and M. Massot, Beyond pressureless gas dynamics : quadrature-based velocity moment models, Comm. Math. Sci. (CMS), vol 10(4), pp 1241-1272 (2012).
  87. I. Gallagher, G. Koch and F. Planchon, A profile decomposition approach to the $L^\infty_t(L^{3}_x)$ Navier-Stokes regularity criterion, Mathematische Annalen 355 (2013), no. 4, 1527–1559 (Arxiv link).
  88. R. Raynaud, E. Dormy Intermittency in spherical Couette dynamos Physical Review E 87, 033011, 2013. doi:10.1103/PhysRevE.87.033011
  89. D. Arsénio, From Boltzmann's equation to the incompressible Navier-Stokes-Fourier system with long-range interactions, Arch. Ration. Mech. Anal. 206 (2012), no. 2, 367-488.
  90. F. Coquel, E. Godlewski and N. Seguin, Relaxation of fluid systems, Mathematical Models and Methods in Applied Sciences (M3AS), volume 22(8), 2012.
  91. I. Gallagher, Th. Paul and L. Saint-Raymond, On the propagation of oceanic waves driven by a strong macroscopic flow, to appear in Abel Symposia Series(Arxiv link).
  92. C. Chalons , F. Coquel, P. Engel, C. Rohde, Fast relaxation solver for hyperbolic-elliptic phase-transition problems, SIAM J. Sci. Comput. (SISC), vol 34(3), A1753-A1776 (2012).
  93. C. Gissinger, L. Petitdemange, M. Schrinner, E. Dormy Bistability between Equatorial and Axial Dipoles during Magnetic Field Reversals Phys. Rev. Lett. 108, 234501, 2012 doi:10.1103/PhysRevLett.108.234501
  94. E. Feireisl, I. Gallagher and A. Novotny, A singular limit for compressible rotating fluids, SIAM Journal for Mathematical Analysis 44 (2012), 192-205 (Arxiv link).
  95. A. Ambroso, C. Chalons and P.-A. Raviart, A Godunov-type method for the seven-equation model of compressible two-phase flow, Computers and Fluids, vol 54, pp 67-91 51 (2012).
  96. D. Bucur, A.L. Dalibard and D. Gerard-Varet, Wall laws for viscous fluids near rough surfaces, ESAIM: Proc. 37 (2012) pp. 117-135.
  97. D. Arsénio and N. Masmoudi, Regularity of renormalized solutions in the Boltzmann equation with long-range interactions, Comm. Pure Appl. Math. 65 (2012), no. 4, 508-548.
  98. A.L. Dalibard and D. Gerard-Varet , Effective boundary condition at a rough surface starting from a slip condition, J. Differential Equations 251 (2011), pp. 3450–3487 (ArXiv link).
  99. J. Morin, E. Dormy, M. Schrinner, J.-F. Donati, Weak- and strong-field dynamos: from the Earth to the stars, Monthly Notices of the Royal Astronomical Society: Letters, 418, 1, L133-L137, 2011. doi:10.1111/j.1745-3933.2011.01159.x
  100. E. Dumas and F. Sueur, Cauchy problem and quasi-stationary limit for the Maxwell-Landau-Lifschitz and Maxwell-Bloch equations, Annali della Scuola Normale Superiore di Pisa, Classe di Scienze,Vol. XI, issue 3, p503-543, 2012 (Arxiv link).
  101. D. Arsénio and L. Saint-Raymond, Compactness in kinetic transport equations and hypoellipticity, J. Funct. Anal. 261 (2011), no. 10, 3044-3098 (Arxiv link).
  102. D. Kah, A. Vié, C. Chalons and M. Massot, Second-order scheme for quadrature-based velocity high-order moment methods for disperse two-phase flows, Annual Research Briefs 2011, Center for Turbulence Research, Stanford University (Available here).
  103. C. Chalons and F. Coquel, Computing material fronts with a Lagrange-Projection approach, Hyperbolic Problems: Theory, Numerics, Applications. Eleventh international conference, Beijing, Series in Contemporary Applied Mathematics (2012).
  104. Ch. Cheverry, I. Gallagher, Th. Paul and L. Saint-Raymond, Semiclassical and spectral analysis of oceanic waves, Duke Mathematical Journal 161 (2012), 845-892 (Arxiv link).
  105. O. Glass, T. Takahashi and F. Sueur, Smoothness of the motion of a rigid body immersed in an incompressible perfect fluid, Annales Scientifiques de l'Ecole Normale Superieure,Volume 45, No.1, p1-51, 2012 (Arxiv link).
  106. B. Després, F. Lagoutière and N. Seguin, Weak solutions to Friedrichs systems with convex constraints, Nonlinearity, volume 24, pages 3055-3081, 2011.
  107. M. Schrinner, L. Petitdemange, E.Dormy, Oscillatory dynamos and their induction mechanisms, Astronomy and Astrophysics, 530, A140, 2011 (doi:10.1051/0004-6361/201016372
  108. D. Arsénio, On the global existence of mild solutions to the Boltzmann equation for small data in $L^D$, Comm. Math. Phys. 302 (2011), no. 2, 453-476.
  109. J.-Y. Chemin, I. Gallagher and P. Zhang, On large perturbations to global solutions of the 3-D incompressible Navier-Stokes equations, to appear in Journal für die reine und angewandte Mathematik (Arxiv link).
  110. A.L. Dalibard, Stability of periodic stationary solutions of scalar conservation laws with space-periodic flux, J. Eur. Math. Soc. (JEMS) 13 (2011), pp. 1245–1288 (arXiv link).