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
相关论文
共 101 条
[1]   Cauchy theory for the gravity water waves system with non-localized initial data [J].
Alazard, T. ;
Burq, N. ;
Zuily, C. .
ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE, 2016, 33 (02) :337-395
[2]   On the Cauchy problem for gravity water waves [J].
Alazard, T. ;
Burq, N. ;
Zuily, C. .
INVENTIONES MATHEMATICAE, 2014, 198 (01) :71-163
[3]   ON THE WATER-WAVE EQUATIONS WITH SURFACE TENSION [J].
Alazard, T. ;
Burq, N. ;
Zuily, C. .
DUKE MATHEMATICAL JOURNAL, 2011, 158 (03) :413-499
[4]  
Alazard T., 2015, ASTERISQUE, V374, P41
[5]  
Alazard T., 2014, SEM L SCHWARTZ EQ DE
[6]  
Alazard T., 2017, Ann. PDE, V3, P17, DOI [10.1007/s40818-017-0032-x, DOI 10.1007/S40818-017-0032-X]
[7]  
Alazard T, 2015, ANN SCI ECOLE NORM S, V48, P1149
[8]   The Water-Wave Equations: From Zakharov to Euler [J].
Alazard, Thomas ;
Burq, Nicolas ;
Zuily, Claude .
STUDIES IN PHASE SPACE ANALYSIS WITH APPLICATIONS TO PDES, 2013, 84 :1-20
[9]   Gravity Capillary Standing Water Waves [J].
Alazard, Thomas ;
Baldi, Pietro .
ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 2015, 217 (03) :741-830
[10]   STRICHARTZ ESTIMATES FOR WATER WAVES [J].
Alazard, Thomas ;
Burq, Nicolas ;
Zuily, Claude .
ANNALES SCIENTIFIQUES DE L ECOLE NORMALE SUPERIEURE, 2011, 44 (05) :855-903
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