On the Rayleigh-Taylor Instability for the two-Phase Navier-Stokes Equations
On the Rayleigh-Taylor Instability for the two-Phase Navier-Stokes Equations
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DOI：
10.1512/iumj.2010.59.4145
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发表时间：
2009-08
期刊：
影响因子：
--
通讯作者：
Jan Pruess;G. Simonett
中科院分区：
文献类型：
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作者：
Jan Pruess;G. Simonett
考虑了初始界面接近平衡状态下，具有表面张力和下压力重力的Navier-Stokes方程组的两相自由边界问题。当重流体位于轻流体之上时，该问题的边界符号在不稳定半平面中存在零点，这导致了著名的瑞利-泰勒不稳定性。利用亨利的一个抽象的不稳定性结果，在L_p$-背景下严格地证明了不稳定性.
The two-phase free boundary problem with surface tension and downforce gravity for the Navier-Stokes system is considered in a situation where the initial interface is close to equilibrium. The boundary symbol of this problem admits zeros in the unstable halfplane in case the heavy fluid is on top of the light one, which leads to the well-known Rayleigh-Taylor instability. Instability is proved rigorously in an $L_p$-setting by means of an abstract instability result due to Henry.