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Stability of the viscoelastic Rayleigh–Taylor problem with internal surface tension
Nonlinear Analysis: Real World Applications ( IF 1.8 ) Pub Date : 2020-06-11 , DOI: 10.1016/j.nonrwa.2020.103170
Youyi Zhao , Weiwei Wang , Junying Cao

We investigate the stability of the Rayleigh–Taylor (RT) problem for stratified viscoelastic fluids with internal surface tension. More precisely, under the stability condition Dis(ϑ,κ)<1, we prove the existence of unique strong solution with exponential decay in time for the (stratified) viscoelastic RT (VRT) problem with proper initial data in Lagrangian coordinates. This shows that a sufficiently large elasticity coefficient or a sufficiently large surface tension coefficient has a stabilizing effect so that it can inhibit the development of (stratified) RT instability.



中文翻译:

内表面张力的粘弹性瑞利泰勒问题的稳定性

我们研究具有内表面张力的分层粘弹性流体的瑞利-泰勒(RT)问题的稳定性。更确切地说,在稳定条件下迪斯ϑκ<1个,我们证明了(分层)粘弹性RT(VRT)问题在拉格朗日坐标中具有适当初始数据的情况下,存在随时间呈指数衰减的唯一强解的存在。这表明足够大的弹性系数或足够大的表面张力系数具有稳定作用,从而可以抑制(分层的)RT不稳定性的发展。

更新日期:2020-06-11
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