A Priori Estimates for the Free-Boundary 3D Compressible Euler Equations in Physical Vacuum

被引：76

作者：

Coutand, Daniel ^{[1
,2
]}

Lindblad, Hans ^{[3
]}

Shkoller, Steve ^{[4
]}

机构：

[1] Heriot Watt Univ, CANPDE, Maxwell Inst Math Sci, Edinburgh EH14 4AS, Midlothian, Scotland

[2] Heriot Watt Univ, Dept Math, Edinburgh EH14 4AS, Midlothian, Scotland

[3] Univ Calif San Diego, Dept Math, San Diego, CA 92093 USA

[4] Univ Calif Davis, Dept Math, Davis, CA 95616 USA

来源：

COMMUNICATIONS IN MATHEMATICAL PHYSICS | 2010年 / 296卷 / 02期

基金：

英国工程与自然科学研究理事会;

关键词：

WELL-POSEDNESS; SURFACE-TENSION; MOTION;

D O I：

10.1007/s00220-010-1028-5

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

We prove a priori estimates for the three-dimensional compressible Euler equations with moving physical vacuum boundary, with an equation of state given by p(rho) = C (gamma) rho (gamma) for gamma > 1. The vacuum condition necessitates the vanishing of the pressure, and hence density, on the dynamic boundary, which creates a degenerate and characteristic hyperbolic free-boundary system to which standard methods of symmetrizable hyperbolic equations cannot be applied.

引用

页码：559 / 587

页数：29

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