关于两相欧拉方程在表面张力和密度比趋于零时的极限
偏微分方程分析
2011-03-08 v2
摘要
我们考虑两种密度分别为和的理想不可压缩流体的自由边界运动，它们由一个不连续面分隔，在该面上压力跳跃与平均曲率成正比，比例因子为。假设瑞利-泰勒符号条件且，我们证明了在和上一致的能量估计。作为推论，我们得到了当和趋于零时，界面问题的解收敛到无表面张力真空自由边界欧拉方程的解。
引用
@article{arxiv.0912.3296,
title = {On the limit as the surface tension and density ratio tend to zero for the two-phase Euler equations},
author = {Fabio Pusateri},
journal= {arXiv preprint arXiv:0912.3296},
year = {2011}
}
备注
Revised version, to appear. In the condition $\rho_- \leq \epsilon^{7/3}$, the exponent is now improved to 3/2. The vorticity of the outer velocity field has been added to the Energy, and a few arguments have been changed accordingly. Other minor changes. Typos corrected