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

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.

Automated summary

This paper focuses on generally symmetric hyperbolic-parabolic systems with Korteweg-type dispersion, proposing new structural conditions and developing a dissipative mechanism of regularity-gain type. Several concrete model systems are checked for compliance with the general structural conditions, including the compressible Navier-Stokes(-Fourier)-Korteweg system. Additionally, the optimality of the general theory on dissipative structure is verified through the calculation of asymptotic expansions of eigenvalues.