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.
引用
收藏
页数：134
相关论文
共 78 条
  • [1] Low mach number limit of the full Navier-Stokes equations
    Alazard, T
    [J]. ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 2006, 180 (01) : 1 - 73
  • [2] Cauchy theory for the gravity water waves system with non-localized initial data
    Alazard, T.
    Burq, N.
    Zuily, C.
    [J]. ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE, 2016, 33 (02): : 337 - 395
  • [3] On the Cauchy problem for gravity water waves
    Alazard, T.
    Burq, N.
    Zuily, C.
    [J]. INVENTIONES MATHEMATICAE, 2014, 198 (01) : 71 - 163
  • [4] Alazard T, 2005, ADV DIFFERENTIAL EQU, V10, P19
  • [5] A MINICOURSE ON THE LOW MACH NUMBER LIMIT
    Alazard, Thomas
    [J]. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S, 2008, 1 (03): : 365 - 404
  • [6] Alazard T, 2015, ANN SCI ECOLE NORM S, V48, P1149
  • [7] Alinhac S., 1989, COMMUN PART DIFF EQ, V14, P173
  • [8] Bahouri H, 2011, GRUNDLEHR MATH WISS, V343, P1, DOI 10.1007/978-3-642-16830-7_1
  • [9] THE INITIAL VALUE-PROBLEM FOR THE NAVIER-STOKES EQUATIONS WITH A FREE-SURFACE
    BEALE, JT
    [J]. COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1981, 34 (03) : 359 - 392
  • [10] On the well-posedness for the Euler-Korteweg model in several space dimensions
    Benzoni-Gavage, S.
    Danchin, R.
    Descombes, S.
    [J]. INDIANA UNIVERSITY MATHEMATICS JOURNAL, 2007, 56 (04) : 1499 - 1579
12345678