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

Miho Murata; Yoshihiro Shibata

doi:10.1137/19M1282076

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

Miho Murata, Yoshihiro Shibata

School of Fundamental Science and Engineering

Research output: Contribution to journal › Article › peer-review

11 Citations (Scopus)

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 R ^N, 3 ≤ N ≤ 7. In this study, the main tools are the maximal Lp-Lq regularity and Lp-Lq decay properties of solutions to the linearized equations.

Original language	English
Pages (from-to)	6313-6337
Number of pages	25
Journal	SIAM Journal on Mathematical Analysis
Volume	52
Issue number	6
DOIs	https://doi.org/10.1137/19M1282076
Publication status	Published - 2020 Dec 17

Keywords

Global well-posedness
Long-time behavior
Maximal regularity
Navier-Stokes-Korteweg system

ASJC Scopus subject areas

Analysis
Computational Mathematics
Applied Mathematics

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10.1137/19M1282076

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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 R N, 3 ≤ N ≤ 7. In this study, the main tools are the maximal Lp-Lq regularity and Lp-Lq decay properties of solutions to the linearized equations.",

keywords = "Global well-posedness, Long-time behavior, Maximal regularity, Navier-Stokes-Korteweg system",

author = "Miho Murata and Yoshihiro Shibata",

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N2 - 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 R N, 3 ≤ N ≤ 7. In this study, the main tools are the maximal Lp-Lq regularity and Lp-Lq decay properties of solutions to the linearized equations.

AB - 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 R N, 3 ≤ N ≤ 7. In this study, the main tools are the maximal Lp-Lq regularity and Lp-Lq decay properties of solutions to the linearized equations.

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

Abstract

Keywords

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