On the isothermal compressible multi-component mixture flow

The local existence and maximal Lp−Lq regularity of solutions

T. Piasecki, Yoshihiro Shibata, E. Zatorska

Research output: Contribution to journalArticle

Abstract

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.

Original languageEnglish
Article number111571
JournalNonlinear Analysis, Theory, Methods and Applications
Volume189
DOIs
Publication statusPublished - 2019 Dec 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

Keywords

  • Local well-posedness
  • Maximal regularity
  • Multicomponent flow

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

Cite this

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abstract = "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.",
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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

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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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