Large-time behavior of solutions to an inflow problem for the compressible Navier-Stokes-Korteweg equations in the half space
type: Item
instance of: scholarly article
title: Large-time behavior of solutions to an inflow problem for the compressible Navier-Stokes-Korteweg equations in the half space
zbMATH Open document ID: 1501.76066
author: Yeping Li
author: Zhengzheng Chen
published in: Journal of Mathematical Fluid Mechanics
publication date: 2022-10-14T00:00:00Z
review text: The authors study the one-dimensional compressible Navier-Stokes-Korteweg system for density and velocity of an adiabatic flow. The focus is on the large-time behaviour of solutions to the inflow problem: the boundary data are given at \(x=0\), and the spatial domain is \(x>0\). Another boundary condition is a finite limit at infinity. Existence of the boundary-layer solution is established, and its stability is proved for ``small'' boundary data.
reviewed by: Ilya A. Chernov
Mathematics Subject Classification ID: 76N10
Mathematics Subject Classification ID: 76N06
Mathematics Subject Classification ID: 35Q30
zbMATH DE Number: 7601576
zbMATH Keywords: internal capillarity
zbMATH Keywords: adiabatic inflow problem
zbMATH Keywords: boundary-layer solution
zbMATH Keywords: energy method
zbMATH Keywords: Poincaré inequality
zbMATH Keywords: spatial decay estimate
zbMATH Keywords: stability
MaRDI profile type: Publication
full work available at URL: s00021-022-00736-w
OpenAlex ID: W4296826836
cites work: Vanishing Capillarity Limit of the Compressible Fluid Models of Korteweg Type to the Navier--Stokes Equations
cites work: Applications of centre manifold theory
cites work: Asymptotic stability of strong rarefaction waves for the compressible fluid models of Korteweg type
cites work: Global classical solutions to the one-dimensional compressible fluid models of Korteweg type with large initial data
cites work: Existence of a global strong solution and vanishing capillarity-viscosity limit in one dimension for the Korteweg system
cites work: Asymptotic Behavior of Solutions to An Impermeable Wall Problem of the Compressible Fluid Models of Korteweg Type with Density-dependent Viscosity and Capillarity
cites work: Nonlinear stability of traveling wave solutions for the compressible fluid models of Korteweg type
cites work: Asymptotic stability of viscous shock profiles for the 1D compressible Navier-Stokes-Korteweg system with boundary effect
cites work: On the thermomechanics of interstitial working
cites work: Inflow problem for the one-dimensional compressible Navier-Stokes equations under large initial perturbation
cites work: Solutions for Two-Dimensional System for Materials of Korteweg Type
cites work: Global solutions of a high dimensional system for Korteweg materials
cites work: On compressible Korteweg fluid-like materials
cites work: Stationary solutions to outflow problem for 1-d compressible fluid models of Korteweg type: existence, stability and convergence rate
cites work: Stability of Stationary Solutions to the Inflow Problem for Full Compressible Navier--Stokes Equations with a Large Initial Perturbation
cites work: Stability of boundary layer and rarefaction wave to an outflow problem for compressible Navier-Stokes equations under large perturbation
cites work: Viscous shock wave and boundary layer solution to an inflow problem for compressible viscous gas
cites work: Asymptotic behavior of solutions to the full compressible Navier-Stokes equations in the half space
cites work: Asymptotic stability of the stationary solution to the compressible Navier-Stokes equations in the half space
cites work: Asymptotic stability of rarefaction wave for the Navier-Stokes equations for a compressible fluid in the half-space
cites work: Asymptotic stability of nonlinear wave for the compressible Navier-Stokes equations in the half space
cites work: Strong solutions for a compressible fluid model of Korteweg type
cites work: Existence and time-asymptotics of global strong solutions to dynamic Korteweg models
cites work: Global existence and optimal decay rate of the compressible Navier-Stokes-Korteweg equations with external force
cites work: Stability of the planar rarefaction wave to two‐dimensional Navier‐Stokes‐Korteweg equations of compressible fluids
cites work: Zero‐viscosity‐capillarity limit to rarefaction waves for the 1D compressible Navier–Stokes–Korteweg equations
cites work: Stability of the planar rarefaction wave to three-dimensional Navier–Stokes–Korteweg equations of compressible fluids
cites work: Asymptotic stability of rarefaction wave for the compressible Navier‐Stokes‐Korteweg equations in the half space
cites work: Zero-viscosity–capillarity limit toward rarefaction wave with vacuum for the Navier–Stokes–Korteweg equations of compressible fluids
cites work: Asymptotic stability of the stationary solution to an out-flow problem for the Navier-Stokes-Korteweg equations of compressible fluids
cites work: Convergence to travelling fronts of solutions of the \(p\)-system with viscosity in the presence of a boundary
cites work: Large-time behaviors of solutions to an inflow problem in the half-space for a one-dimensional system of compressible viscous gas
cites work: Global asymptotics toward the rarefaction wave for solutions of viscous 𝑝-system with boundary effect
cites work: Large-Time Behavior of Solutions to the Inflow Problem of Full Compressible Navier–Stokes Equations
cites work: Global existence and asymptotic convergence of weak solutions for the one-dimensional Navier-Stokes equations with capillarity and nonmonotonic pressure
cites work: Large time behavior of solutions to the isentropic compressible fluid models of Korteweg type in \(\mathbb{R}^3\)
cites work: Global existence and optimal \(L^2\) decay rate for the strong solutions to the compressible fluid models of Korteweg type
cites work: Optimal decay rates of the compressible fluid models of Korteweg type
cites work: Optimal decay rates for the compressible fluid models of Korteweg type
cites work: Decay rates of the compressible Navier-Stokes-Korteweg equations with potential forces
DOI: 10.1007/S00021-022-00736-W
description: scientific article; zbMATH DE number 7601576