The Existence of Global Solutions for the Full Navier-Stokes-Korteweg System of van der Waals Gas

The aim of this work is to prove the existence for the global solution of a non-isothermal or non-isentropic model of capillary compressible fluids derived by J. E. Dunn and J. Serrin (1985), in the case of van der Waals gas. Under the small initial perturbation, the proof of the global existence is...

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Bibliographic Details
Published in:Acta mathematica scientia 2023-03, Vol.43 (2), p.469-491
Main Author: Hong, Hakho
Format: Article
Language:English
Subjects:
Analysis
Mathematics
Mathematics and Statistics
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Summary:The aim of this work is to prove the existence for the global solution of a non-isothermal or non-isentropic model of capillary compressible fluids derived by J. E. Dunn and J. Serrin (1985), in the case of van der Waals gas. Under the small initial perturbation, the proof of the global existence is based on an elementary energy method using the continuation argument of local solution. Moreover, the uniqueness of global solutions and large time behavior of the density are given. It is one of the main difficulties that the pressure p is not the increasing function of the density ρ .
ISSN:0252-9602
1572-9087
DOI:10.1007/s10473-023-0201-9