On the isothermal compressible multi-component mixture flow: The local existence and maximal Lp−Lq regularity of solutions

T. Piasecki, Yoshihiro Shibata, E. Zatorska

研究成果: Article

1 引用 (Scopus)

抄録

We consider the initial–boundary value problem for the system of equations describing the flow of compressible isothermal mixture of arbitrary large number of components. The system consists of the compressible Navier–Stokes equations and a subsystem of diffusion equations for the species. The subsystems are coupled by the form of the pressure and the strong cross-diffusion effects in the diffusion fluxes of the species. Assuming the existence of solutions to the symmetrized and linearized equations, proven in Piasecki, Shibata and Zatorska (2019), we derive the estimates for the nonlinear equations and prove the local-in-time existence and maximal Lp−Lq regularity of solutions.

元の言語English
記事番号111571
ジャーナルNonlinear Analysis, Theory, Methods and Applications
189
DOI
出版物ステータスPublished - 2019 12 1

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Maximal Regularity
Regularity of Solutions
Local Existence
Subsystem
Cross-diffusion
Compressible Navier-Stokes Equations
Number of Components
Diffusion equation
System of equations
Existence of Solutions
Nonlinear Equations
Nonlinear equations
Arbitrary
Estimate
Fluxes
Form

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

これを引用

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T2 - The local existence and maximal Lp−Lq regularity of solutions

AU - Piasecki, T.

AU - Shibata, Yoshihiro

AU - Zatorska, E.

PY - 2019/12/1

Y1 - 2019/12/1

N2 - We consider the initial–boundary value problem for the system of equations describing the flow of compressible isothermal mixture of arbitrary large number of components. The system consists of the compressible Navier–Stokes equations and a subsystem of diffusion equations for the species. The subsystems are coupled by the form of the pressure and the strong cross-diffusion effects in the diffusion fluxes of the species. Assuming the existence of solutions to the symmetrized and linearized equations, proven in Piasecki, Shibata and Zatorska (2019), we derive the estimates for the nonlinear equations and prove the local-in-time existence and maximal Lp−Lq regularity of solutions.

AB - We consider the initial–boundary value problem for the system of equations describing the flow of compressible isothermal mixture of arbitrary large number of components. The system consists of the compressible Navier–Stokes equations and a subsystem of diffusion equations for the species. The subsystems are coupled by the form of the pressure and the strong cross-diffusion effects in the diffusion fluxes of the species. Assuming the existence of solutions to the symmetrized and linearized equations, proven in Piasecki, Shibata and Zatorska (2019), we derive the estimates for the nonlinear equations and prove the local-in-time existence and maximal Lp−Lq regularity of solutions.

KW - Local well-posedness

KW - Maximal regularity

KW - Multicomponent flow

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