Local-in-time existence of a free-surface 3D Euler flow with H 2+d initial vorticity in a neighborhood of the free boundary

被引：3

作者：

Kukavica, I ^{[1
]}

Ozanski, W. S. ^{[2
,3
]}

机构：

[1] Univ Southern Calif, Dept Math, Los Angeles, CA USA

[2] Florida State Univ, Dept Math, Tallahassee, FL 32306 USA

[3] Polish Acad Sci, Inst Math, PL-00656 Warsaw, Poland

来源：

NONLINEARITY | 2023年 / 36卷 / 01期

关键词：

Euler equations; free boundary; Lagrangian coordinates; NAVIER-STOKES EQUATIONS; 2-DIMENSIONAL WATER-WAVES; WELL-POSEDNESS; GLOBAL-SOLUTIONS; INCOMPRESSIBLE LIQUID; UNIFORM REGULARITY; SOBOLEV SPACES; TENSION LIMIT; GRAVITY; MOTION;

D O I：

10.1088/1361-6544/aca5e3

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider the three-dimensional Euler equations in a domain with a free boundary with no surface tension. We assume that u(0)is an element of H2.5+delta is such that curl u(0) is an element of H2+delta in an arbitrarily small neighborhood of the free boundary, and we use the Lagrangian approach to derive an a priori estimate that can be used to prove local-in-time existence and uniqueness of solutions under the Rayleigh-Taylor stability condition.

引用

页码：636 / 652

页数：17

共 52 条

[1] ON THE WATER-WAVE EQUATIONS WITH SURFACE TENSION [J].