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

Part of: Equations of mathematical physics and other areas of application Compressible fluids and gas dynamics, general

Published online by Cambridge University Press:  11 October 2021

Xiaopeng Zhao
Xiaopeng Zhao*
Affiliation:
College of Sciences, Northeastern University, Shenyang 110004, China (zhaoxiaopeng@jiangnan.edu.cn)
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Abstract

We study the small data global well-posedness and time-decay rates of solutions to the Cauchy problem for three-dimensional 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 $\dot {H}^{-s}$($0\leq s<\frac {3}{2}$) negative Sobolev norms is shown to be preserved along time evolution and enhance the decay rates.

Keywords

Compressible Navier–Stokes–Allen–Cahn equationsdecay estimatesglobal well-posednesspure energy method

MSC classification

Primary: 35Q30: Navier-Stokes equations
Secondary: 76N10: Existence, uniqueness, and regularity theory
Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 152 , Issue 5 , October 2022 , pp. 1291 - 1322
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Copyright
Copyright © The Author(s), 2021. Published by Cambridge University Press on behalf of The Royal Society of Edinburgh

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