On some two phase problem for compressible and compressible viscous fluid flow separated by sharp interface

Takayuki Kubo, Yoshihiro Shibata, Kohei Soga

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

In this paper, we prove a local in time unique existence theorem for some two phase problem of compressible and compressible barotropic viscous fluid flow without surface tension in the Lp in time and the Lq in space framework with 2 <p <1 and N <q <∞ under the assumption that the initial domain is a uniform Wq 2-1/q domain in ℝN(N ≥ 2). After transforming a unknown time dependent domain to the initial domain by the Lagrangian transformation, we solve the problem by the contraction mapping principle with the maximal Lp-Lq regularity of the generalized Stokes operator for the compressible viscous fluid flow with free boundary condition. The key step of our method is to prove the existence of R-bounded solution operator to resolvent problem corresponding to linearized problem. The R-boundedness combined with Weis's operator valued Fourier multiplier theorem implies the generation of analytic semigroup and the maximal Lp-Lq regularity theorem.

Original languageEnglish
Pages (from-to)3741-3774
Number of pages34
JournalDiscrete and Continuous Dynamical Systems
Volume36
Issue number7
DOIs
Publication statusPublished - 2016 Jul 1

Fingerprint

Compressible Fluid
Viscous Flow
Viscous Fluid
Fluid Flow
Flow of fluids
Surface tension
Operator-valued Fourier multipliers
R-boundedness
Regularity
Boundary conditions
Stokes Operator
Contraction Mapping Principle
Analytic Semigroup
Bounded Solutions
Resolvent
Free Boundary
Theorem
Surface Tension
Existence Theorem
Imply

Keywords

  • Compressible viscous fluid
  • Free boundary problem
  • Local well-posedness theorem
  • Maximal L-L regularity
  • R-bounded solution operator
  • Two phase problem
  • Uniform W domain

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Applied Mathematics
  • Analysis

Cite this

On some two phase problem for compressible and compressible viscous fluid flow separated by sharp interface. / Kubo, Takayuki; Shibata, Yoshihiro; Soga, Kohei.

In: Discrete and Continuous Dynamical Systems, Vol. 36, No. 7, 01.07.2016, p. 3741-3774.

Research output: Contribution to journalArticle

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