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arXiv · 1910.09432

Global well-posedness and decay estimates for three-dimensional compressible Navier-Stokes-Allen-Cahn system

Xiaopeng Zhao
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Abstract

We study the small data global well-posedness and time-decay rates of solutions to the Cauchy problem for 3D compressible Navier-Stokes-Allen-Cahn equations via a refined pure energy method. In particular, the optimal decay rates of the higher-order spatial derivatives of the solution are obtained, the $\dot{H}^{-s}$ ($0\leq s<\frac32$) negative Sobolev norms is shown to be preserved along time evolution and enhance the decay rates.

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Xiaopeng Zhao. 2019-10-15. Global well-posedness and decay estimates for three-dimensional compressible Navier-Stokes-Allen-Cahn system. https://arxiv.org/abs/1910.09432

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