The global well-posedness for the compressible fluid model of Korteweg type

Miho Murata; Yoshihiro Shibata

The global well-posedness for the compressible fluid model of Korteweg type

Analysis of PDEs 2019-08-21 v1

Authors: Miho Murata , Yoshihiro Shibata

Abstract

In this paper, we consider the compressible fluid model of Korteweg type which can be used as a phase transition model. It is shown that the system admits a unique, global strong solution for small initial data in $\mathbb R^N$ , $N \geq 3$ . In this study, the main tools are the maximal $L_p$ - $L_q$ regularity and $L_p$ - $L_q$ decay properties of solutions to the linearized equations.

Keywords

compressible fluid korteweg type global well-posedness strong solution maximal lp-lq regularity

Cite

@article{arxiv.1908.07224,
  title  = {The global well-posedness for the compressible fluid model of Korteweg type},
  author = {Miho Murata and Yoshihiro Shibata},
  journal= {arXiv preprint arXiv:1908.07224},
  year   = {2019}
}

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