Dissipative structure for symmetric hyperbolic-parabolic systems with Korteweg-type dispersion. Issue 2 (7th February 2022) - Kawashima, Shuichi; Shibata, Yoshihiro; Xu, Jiang
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.