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

T. Piasecki; Y. Shibata; E. Zatorska

doi:10.1016/j.na.2019.111571

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

T. Piasecki, Y. Shibata^*, E. Zatorska

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

13 Citations (Scopus)

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 L_p−L_q regularity of solutions.

Original language	English
Article number	111571
Journal	Nonlinear Analysis, Theory, Methods and Applications
Volume	189
DOIs	https://doi.org/10.1016/j.na.2019.111571
Publication status	Published - 2019 Dec
Externally published	Yes

Keywords

Local well-posedness
Maximal regularity
Multicomponent flow

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.1016/j.na.2019.111571

Cite this

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

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.",

keywords = "Local well-posedness, Maximal regularity, Multicomponent flow",

author = "T. Piasecki and Y. Shibata and E. Zatorska",

note = "Funding Information: Supported by the Top Global University Project and the Polish National Science Centre grant 2018/29/B/ST1/00339.Adjunct faculty member in the Department of Mechanical Engineering and MaterialsScience, University of Pittsburgh. Partially supported by JSPS Grant-in-aid for Scientific Research (A) 17H0109 and Top Global University Project.Supported by the Top Global University Project and the Polish Government MNiSW research grant 2016–2019 ”Iuventus Plus” No. 0888/IP3/2016/74. Publisher Copyright: {\textcopyright} 2019",

year = "2019",

month = dec,

doi = "10.1016/j.na.2019.111571",

language = "English",

volume = "189",

journal = "Nonlinear Analysis, Theory, Methods and Applications",

issn = "0362-546X",

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

AU - Piasecki, T.

AU - Shibata, Y.

AU - Zatorska, E.

N1 - Funding Information: Supported by the Top Global University Project and the Polish National Science Centre grant 2018/29/B/ST1/00339.Adjunct faculty member in the Department of Mechanical Engineering and MaterialsScience, University of Pittsburgh. Partially supported by JSPS Grant-in-aid for Scientific Research (A) 17H0109 and Top Global University Project.Supported by the Top Global University Project and the Polish Government MNiSW research grant 2016–2019 ”Iuventus Plus” No. 0888/IP3/2016/74. Publisher Copyright: © 2019

PY - 2019/12

Y1 - 2019/12

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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