TY - JOUR
T1 - Dissipative structure for symmetric hyperbolic-parabolic systems with Korteweg-type dispersion
AU - Kawashima, Shuichi
AU - Shibata, Yoshihiro
AU - Xu, Jiang
N1 - Funding Information:
This work is partially supported by Top Global University Project and Toyota Central Research Institute Joint Research Fund. S. Kawashima is partially supported by JSPS KAKENHI Grant Numbers JP18H01131, JP19H05597, and JP20H00118. Y. Shibata is partially supported by JSPS KAKENHI Grant Number JP17H0109. J. Xu is partially supported by the National Natural Science Foundation of China (11871274, 12031006) and the China Scholarship Council (201906835023).
Publisher Copyright:
© 2021 Taylor & Francis Group, LLC.
PY - 2022
Y1 - 2022
N2 - 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.
AB - 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.
KW - Decay property
KW - Euler-Fourier-Korteweg system
KW - Korteweg-type dispersion
KW - Navier-Stokes-Fourier-Korteweg system
KW - dissipative structure
KW - hyperbolic-parabolic systems
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U2 - 10.1080/03605302.2021.1983596
DO - 10.1080/03605302.2021.1983596
M3 - Article
AN - SCOPUS:85116758499
SN - 0360-5302
VL - 47
SP - 378
EP - 400
JO - Communications in Partial Differential Equations
JF - Communications in Partial Differential Equations
IS - 2
ER -