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
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