On the limit as the surface tension and density ratio tend to zero for the two-phase Euler equations
On the limit as the surface tension and density ratio tend to zero for the two-phase Euler equations
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两相欧拉方程表面张力和密度比趋于零时的极限
DOI：
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发表时间：
2009
期刊：
影响因子：
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通讯作者：
F. Pusateri
中科院分区：
文献类型：
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作者：
F. Pusateri
我们考虑两种完全不可压缩流体的自由边界运动，它们具有不同的密度$
ho_+$和$
ho_-$，它们被一个不连续的表面分开，沿着这个表面，压力经历一个与平均曲率成比例的跳跃，其系数$epsilon^2$。假设railleigh - taylor符号条件和$
ho_- leq epsilon^{3/2}$，我们证明了$
ho_-$和$epsilon$的能量估计是均匀的。因此，我们得到了在无表面张力的真空中，当$epsilon$和$
ho_-$趋于零时，界面问题的解收敛于自由边界欧拉方程的解。
We consider the free-boundary motion of two perfect incompressible fluids with different densities $
ho_+$ and $
ho_-$, separated by a surface of discontinuity along which the pressure experiences a jump proportional to the mean curvature by a factor $epsilon^2$. Assuming the Raileigh-Taylor sign condition and $
ho_- leq epsilon^{3/2}$ we prove energy estimates uniform in $
ho_-$ and $epsilon$. As a consequence we obtain convergence of solutions of the interface problem to solutions of the free-boundary Euler equations in vacuum without surface tension as $epsilon$ and $
ho_-$ tend to zero.