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

DOI10.1080/03605302.2021.1983596zbMath1484.35157OpenAlexW3206003149MaRDI QIDQ5037298

Shuichi Kawashima, Yoshihiro Shibata, Jiang Xu

Publication date: 28 February 2022

Published in: Communications in Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/03605302.2021.1983596

zbMATH Keywords

hyperbolic-parabolic systemsdecay propertyasymptotic expansions of eigenvaluesEuler-Fourier-Korteweg systemKorteweg-type dispersionNavier-Stokes-Fourier-Korteweg systemregularity-gain type structure

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) PDEs in connection with fluid mechanics (35Q35) KdV equations (Korteweg-de Vries equations) (35Q53) Systems of nonlinear higher-order PDEs (35G50)

Related Items

Dissipative structure of one-dimensional isothermal compressible fluids of Korteweg type, Symmetrization and local existence of strong solutions for diffuse interface fluid models, Global existence and analyticity of \(L^p\) solutions to the compressible fluid model of Korteweg type

Cites Work

• Unnamed Item
• Unnamed Item
• Existence of global weak solution for compressible fluid models of Korteweg type
• Large time asymptotics for partially dissipative hyperbolic systems
• Zero Mach number limit of the compressible Navier-Stokes-Korteweg equations
• Strong solutions for a compressible fluid model of Korteweg type
• On the thermomechanics of interstitial working
• Systems of equations of hyperbolic-parabolic type with applications to the discrete Boltzmann equation
• On the steady flow of compressible viscous fluid and its stability with respect to initial disturbance.
• Dissipative structure for symmetric hyperbolic systems with memory
• Global solutions of a high dimensional system for Korteweg materials
• The \(L^p\) energy methods and decay for the compressible Navier-Stokes equations with capillarity
• Global well-posedness and time-decay estimates of the compressible Navier-Stokes-Korteweg system in critical Besov spaces
• Decay property for symmetric hyperbolic system with memory-type diffusion
• Decay structure for symmetric hyperbolic systems with non-symmetric relaxation and its application
• On the maximal \(L_p-L_q\) regularity for a compressible fluid model of Korteweg type on general domains
• Optimal decay rates for the compressible fluid models of Korteweg type
• Existence and nonlinear stability of stationary solutions to the full compressible Navier-Stokes-Korteweg system
• Local in time results for local and non-local capillary Navier-Stokes systems with large data
• Finite Energy Method for Compressible Fluids: The Navier‐Stokes‐Korteweg Model
• On the decay of solutions to the linearized equations of electro-magneto-fluid dynamics
• Large-time behaviour of solutions to hyperbolic–parabolic systems of conservation laws and applications
• Solutions for Two-Dimensional System for Materials of Korteweg Type
• New structural conditions on decay property with regularity-loss for symmetric hyperbolic systems with non-symmetric relaxation
• On Some Compressible Fluid Models: Korteweg, Lubrication, and Shallow Water Systems
• Dissipative structure and asymptotic profiles for symmetric hyperbolic systems with memory
• The Global Well-Posedness for the Compressible Fluid Model of Korteweg Type
• Vanishing Capillarity Limit of the Compressible Fluid Models of Korteweg Type to the Navier--Stokes Equations
• Systems of Conservation Equations with a Convex Extension
• Existence of solutions for compressible fluid models of Korteweg type