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

Abstract

In this paper, we are concerned with generally symmetric hyperbolic-parabolic systems with Korteweg-type dispersion. Referring to those classical efforts in 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
JournalCommunications in Partial Differential Equations
DOIs
Publication statusAccepted/In press - 2021

Keywords

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

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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