Miho Murata, Yoshihiro Shibata
Published 2019-08-20Version 1
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.
Global existence and analyticity of $L^p$ solutions to the compressible fluid model of Korteweg type
The global well-posedness of the compressible fluid model of Korteweg type for the critical case
Compressible fluid model of Korteweg type with free boundary condition: model problem
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