Dissipative structure for symmetric hyperbolic-parabolic systems with Korteweg-type dispersion

Shuichi Kawashima, Yoshihiro Shibata, Jiang Xu*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

Abstract

In this paper, we are concerned with generally symmetric hyperbolic-parabolic systems with Korteweg-type dispersion. Referring to those classical efforts by Kawashima et al., we formulate new structural conditions for the Korteweg-type dispersion and develop the dissipative mechanism of “regularity-gain type.” As an application, it is checked that several concrete model systems (e.g., the compressible Navier-Stokes(-Fourier)-Korteweg system) satisfy the general structural conditions. In addition, the optimality of our general theory on the dissipative structure is also verified by calculating the asymptotic expansions of eigenvalues.

Original languageEnglish
Pages (from-to)378-400
Number of pages23
JournalCommunications in Partial Differential Equations
Volume47
Issue number2
DOIs
Publication statusPublished - 2022

Keywords

  • Decay property
  • Euler-Fourier-Korteweg system
  • Korteweg-type dispersion
  • Navier-Stokes-Fourier-Korteweg system
  • dissipative structure
  • hyperbolic-parabolic systems

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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