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compressible navier–stokes–allen–cahn equations

Proceedings of the Royal Society of Edinburgh Section A: Mathematics (1)

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1 results

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
Xiaopeng Zhao
Journal:

Proceedings of the Royal Society of Edinburgh. Section A: Mathematics / Volume 152 / Issue 5 / October 2022

Published online by Cambridge University Press:

11 October 2021, pp. 1291-1322

Print publication:

October 2022
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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.