On weak solutions to a dissipative Baer-Nunziato-Type system for a mixture of two compressible heat conducting gases

Young Sam Kwon; Antonin Novotny; C. H. Arthur Cheng

doi:10.1142/S021820252050030X

On weak solutions to a dissipative Baer-Nunziato-Type system for a mixture of two compressible heat conducting gases

Young Sam Kwon, Antonin Novotny, C. H. Arthur Cheng

Department of Mathematics

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

3 Scopus citations

Abstract

In this paper, we consider a compressible dissipative Baer-Nunziato-Type system for a mixture of two compressible heat conducting gases. We prove that the set of weak solutions is stable, meaning that any sequence of weak solutions contains a (weakly) convergent subsequence whose limit is again a weak solution to the original system. Such type of results is usually considered as the most essential step to the proof of the existence of weak solutions. This is the first result of this type in the mathematical literature. Nevertheless, the construction of weak solutions to this system however remains still an (difficult) open problem.

Original language	English
Pages (from-to)	1517-1553
Number of pages	37
Journal	Mathematical Models and Methods in Applied Sciences
Volume	30
Issue number	8
DOIs	https://doi.org/10.1142/S021820252050030X
State	Published - 1 Jul 2020

Keywords

Baer-Nunziato-Type system
Bi-fluid system
compressible Navier-Stokes-Fourier equations
continuity equation
large data weak solution
transport equation

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10.1142/S021820252050030X

The Water Wave Equation and the Incompressible Limit Problems(2/2)
Cheng, C.-H. (PI)
1/08/19 → 31/07/20
Project: Research

Cite this

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AU - Novotny, Antonin

AU - Arthur Cheng, C. H.

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AB - In this paper, we consider a compressible dissipative Baer-Nunziato-Type system for a mixture of two compressible heat conducting gases. We prove that the set of weak solutions is stable, meaning that any sequence of weak solutions contains a (weakly) convergent subsequence whose limit is again a weak solution to the original system. Such type of results is usually considered as the most essential step to the proof of the existence of weak solutions. This is the first result of this type in the mathematical literature. Nevertheless, the construction of weak solutions to this system however remains still an (difficult) open problem.

KW - Baer-Nunziato-Type system

KW - Bi-fluid system

KW - compressible Navier-Stokes-Fourier equations

KW - continuity equation

KW - large data weak solution

KW - transport equation

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On weak solutions to a dissipative Baer-Nunziato-Type system for a mixture of two compressible heat conducting gases

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Keywords

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The Water Wave Equation and the Incompressible Limit Problems(2/2)

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