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Global well-posedness and decay estimates for three-dimensional compressible Navier–Stokes–Allen–Cahn systems
Published online by Cambridge University Press: 11 October 2021
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.
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- Research Article
- Information
- Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 152 , Issue 5 , October 2022 , pp. 1291 - 1322
- Copyright
- Copyright © The Author(s), 2021. Published by Cambridge University Press on behalf of The Royal Society of Edinburgh
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