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

Takayuki Kubo, Yoshihiro Shibata, Kohei Soga

    研究成果: Article

    1 引用 (Scopus)

    抄録

    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.

    元の言語English
    ページ(範囲)3741-3774
    ページ数34
    ジャーナルDiscrete and Continuous Dynamical Systems- Series A
    36
    発行部数7
    DOI
    出版物ステータスPublished - 2016 7 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

    ASJC Scopus subject areas

    • Discrete Mathematics and Combinatorics
    • Applied Mathematics
    • Analysis

    これを引用

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    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 q 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.",
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    TY - JOUR

    T1 - On some two phase problem for compressible and compressible viscous fluid flow separated by sharp interface

    AU - Kubo, Takayuki

    AU - Shibata, Yoshihiro

    AU - Soga, Kohei

    PY - 2016/7/1

    Y1 - 2016/7/1

    N2 - 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 q 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.

    AB - 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 q 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.

    KW - Compressible viscous fluid

    KW - Free boundary problem

    KW - Local well-posedness theorem

    KW - Maximal L-L regularity

    KW - R-bounded solution operator

    KW - Two phase problem

    KW - Uniform W domain

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