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

Xiaopeng Zhao

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

Analysis of PDEs 2021-03-23 v3

Authors: Xiaopeng Zhao

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.

Keywords

compressible navier-stokes-allen-cahn global well-posedness decay estimates cauchy problem energy method negative sobolev norms

Cite

@article{arxiv.1910.09432,
  title  = {Global well-posedness and decay estimates for three-dimensional compressible Navier-Stokes-Allen-Cahn system},
  author = {Xiaopeng Zhao},
  journal= {arXiv preprint arXiv:1910.09432},
  year   = {2021}
}

Comments

28pages, 0 figure. arXiv admin note: text overlap with arXiv:1910.07904 and text overlap with arXiv:1112.4902 by other authors

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