We investigate the stability of the Rayleigh–Taylor (RT) problem for stratified viscoelastic fluids with internal surface tension. More precisely, under the stability condition $\mathrm{Dis}(\vartheta ,\kappa )<1$, 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：

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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$\mathrm{迪斯}（\vartheta ，\kappa ）<\mathrm{1个}$，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。