A PRIORI ESTIMATES FOR THE 3D COMPRESSIBLE FREE-BOUNDARY EULER EQUATIONS WITH SURFACE TENSION IN THE CASE OF A LIQUID

被引：7
作者：
Disconzi, Marcelo M. [1 ]
Kukavica, Igor [2 ]
机构：
[1] Vanderbilt Univ, Dept Math, Nashville, TN 37240 USA
[2] Univ Southern Calif, Dept Math, Los Angeles, CA 91107 USA
来源：
EVOLUTION EQUATIONS AND CONTROL THEORY | 2019年 / 8卷 / 03期
关键词：
Compressible Euler; free-boundary; surface tension; liquid; regularity; GRAVITY WATER-WAVES; INITIAL VALUE-PROBLEM; CURRENT-VORTEX SHEETS; WELL-POSEDNESS; INCOMPRESSIBLE LIQUID; LINEARIZED MOTION; GLOBAL-SOLUTIONS; SPLASH SINGULARITIES; LOCAL EXISTENCE; SOBOLEV SPACES;
D O I：
10.3934/eect.2019025
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We derive a priori estimates for the compressible free-boundary Euler equations with surface tension in three spatial dimensions in the case of a liquid. These are estimates for local existence in Lagrangian coordinates when the initial velocity and initial density belong to H-3, with an extra regularity condition on the moving boundary, thus lowering the regularity of the initial data. Our methods are direct and involve two key elements: the boundary regularity provided by the mean curvature and a new compressible Cauchy invariance.
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收藏
页码：503 / 542
页数：40
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