Incompressible limit for the free surface Navier-Stokes system

被引：1
作者：
Masmoudi, Nader [1 ,2 ]
Rousset, Frederic [3 ]
Sun, Changzhen [4 ,5 ]
机构：
[1] New York Univ Abu Dhabi, NYUAD Res Inst, POB 129188, Abu Dhabi, U Arab Emirates
[2] NYU, Courant Inst Math Sci, 251 Mercer St, New York, NY 10012 USA
[3] Univ Paris Saclay, CNRS, Lab Math Orsay UMR 8628, F-91405 Orsay, France
[4] Univ Toulouse, Inst Math Toulouse, UMR 5219, F-31062 Toulouse 9, France
[5] Univ Paul Sabatier, CNRS, 118 Route Narbonne, F-31062 Toulouse 9, France
来源：
ANNALS OF PDE | 2023年 / 9卷 / 01期
关键词：
Uniform regularity; Low Mach number limit; Free surface viscous fluids; Boundary layer; MACH NUMBER LIMIT; FREE-BOUNDARY PROBLEM; COMPRESSIBLE EULER EQUATIONS; WATER-WAVES SYSTEM; WELL-POSEDNESS; GLOBAL-SOLUTIONS; SINGULAR LIMITS; UNIFORM REGULARITY; EXISTENCE; SLIP;
D O I：
10.1007/s40818-023-00148-7
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We establish uniform regularity estimates with respect to the Mach number for the three-dimensional free surface compressible Navier-Stokes system in the case of slightly well-prepared initial data in the sense that the acoustic components like the divergence of the velocity field are of size v e, e being the Mach number. These estimates allow us to justify the convergence towards the free surface incompressible Navier-Stokes system in the low Mach number limit. One of the main difficulties is the control of the regularity of the surface in presence of boundary layers with fast oscillations.
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页数：134
相关论文
共 78 条
  • [11] Bourguignon J.P., 1974, J FUNCT ANAL, V15, P341, DOI DOI 10.1016/0022-1236(74)90027-5
  • [12] Low Mach number limit of viscous polytropic flows: Formal asymptotics in the periodic case
    Bresch, D
    Desjardins, B
    Grenier, E
    Lin, CK
    [J]. STUDIES IN APPLIED MATHEMATICS, 2002, 109 (02) : 125 - 149
  • [13] Well-posedness of the free-surface incompressible Euler equations with or without surface tension
    Coutand, Daniel
    Shkoller, Steve
    [J]. JOURNAL OF THE AMERICAN MATHEMATICAL SOCIETY, 2007, 20 (03) : 829 - 930
  • [14] WELL-POSEDNESS OF THE FREE-BOUNDARY COMPRESSIBLE 3-D EULER EQUATIONS WITH SURFACE TENSION AND THE ZERO SURFACE TENSION LIMIT
    Coutand, Daniel
    Hole, Jason
    Shkoller, Steve
    [J]. SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 2013, 45 (06) : 3690 - 3767
  • [15] Low Mach number limit for viscous compressible flows
    Danchin, R
    [J]. ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE, 2005, 39 (03): : 459 - 475
  • [16] Zero Mach number limit in critical spaces for compressible Navier-Stokes equations
    Danchin, R
    [J]. ANNALES SCIENTIFIQUES DE L ECOLE NORMALE SUPERIEURE, 2002, 35 (01): : 27 - 75
  • [17] Danchin R, 2016, MATH ANN, V366, P1365, DOI 10.1007/s00208-016-1361-x
  • [18] SINGULAR LIMITS IN COMPRESSIBLE FLUID-DYNAMICS
    DAVEIGA, HB
    [J]. ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 1994, 128 (04) : 313 - 327
  • [19] Global solutions of the gravity-capillary water-wave system in three dimensions
    Deng, Yu
    Ionescu, Alexandru D.
    Pausader, Benoit
    Pusateri, Fabio
    [J]. ACTA MATHEMATICA, 2018, 219 (02) : 213 - 402
  • [20] Incompressible limit for solutions of the isentropic Navier-Stokes equations with Dirichlet boundary conditions
    Desjardins, B
    Grenier, E
    Lions, PL
    Masmoudi, N
    [J]. JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES, 1999, 78 (05): : 461 - 471
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