\(L ^1\) convergence to the Barenblatt solution for compressible Euler equations with damping

DOI10.1007/s00205-010-0355-1zbMath1229.35196OpenAlexW1983294494MaRDI QIDQ717473

Zhen Wang, Ronghua Pan, Fei-Min Huang

Publication date: 4 October 2011

Published in: Archive for Rational Mechanics and Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00205-010-0355-1

zbMATH Keywords

porous mediumdampingDarcy's lawasymptotic behaviourBarenblatt solutioncompressible Euler equation

Mathematics Subject Classification ID

Flows in porous media; filtration; seepage (76S05) Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics (76N10) Euler equations (35Q31)

Related Items (54)

Relative entropy method for the relaxation limit of hydrodynamic models ⋮ Asymptotic stability of solutions to the Hamilton-Jacobi equation ⋮ Asymptotic behavior of solutions to bipolar Euler-Poisson equations with time-dependent damping ⋮ Stabilization effect of frictions for transonic shocks in steady compressible Euler flows passing three-dimensional ducts ⋮ The strong relaxation limit of the multidimensional Euler equations ⋮ Decay properties of solutions toward a multiwave pattern to the Cauchy problem for the scalar conservation law with degenerate flux and viscosity ⋮ Global resolution of the physical vacuum singularity for three-dimensional isentropic inviscid flows with damping in spherically symmetric motions ⋮ Global asymptotics toward the rarefaction waves for solutions to the Cauchy problem of the scalar conservation law with nonlinear viscosity ⋮ Large time behavior and pointwise estimates for compressible Euler equations with damping ⋮ Decay properties of solutions to the Cauchy problem for the scalar conservation law with nonlinearly degenerate viscosity ⋮ Stability and asymptotic analysis for instationary gas transport via relative energy estimates ⋮ Convergence rates to the Barenblatt solutions for the compressible Euler equations with time-dependent damping ⋮ Global existence and convergence rates of solutions for the compressible Euler equations with damping ⋮ Stability of aerostatic equilibria in porous medium flows ⋮ A remark on the multi-dimensional compressible Euler system with damping in the 𝐿^{𝑝} critical Besov spaces ⋮ The time asymptotic expansion for the compressible Euler equations with time-dependent damping ⋮ BV solutions for a hydrodynamic model of flocking-type with all-to-all interaction kernel ⋮ Optimal Decay Rates of the Compressible Euler Equations with Time-Dependent Damping in \({\mathbb {R}}^n\): (II) Overdamping Case ⋮ Absence of singularities in solutions for the compressible Euler equations with source terms in ⋮ Cahn-Hillard and Keller-Segel systems as high-friction limits of Euler-Korteweg and Euler-Poisson equations ⋮ The best asymptotic profile of solutions to Euler equations with time‐dependent damping ⋮ Asymptotic Behavior of Solutions Toward the Viscous Shock Waves to the Cauchy Problem for the Scalar Conservation Law with Nonlinear Flux and Viscosity ⋮ Uniform boundedness in weak solutions to a specific dissipative system ⋮ Convergence to equilibrium in Wasserstein distance for damped Euler equations with interaction forces ⋮ Global existence and convergence to the modified Barenblatt solution for the compressible Euler equations with physical vacuum and time-dependent damping ⋮ From gas dynamics with large friction to gradient flows describing diffusion theories ⋮ Almost global solutions to the three-dimensional isentropic inviscid flows with damping in a physical vacuum around Barenblatt solutions ⋮ Stability of smooth solutions for the compressible Euler equations with time-dependent damping and one-side physical vacuum ⋮ \(L^{1}\)-convergence rates to the Barenblatt solution for the damped compressible Euler equations ⋮ Relaxation to fractional porous medium equation from Euler-Riesz system ⋮ Singularities of solutions to the compressible Euler equations and Euler-Poisson equations with damping ⋮ Convergence to nonlinear diffusion waves for solutions of Euler-Korteweg equations with damping ⋮ Decay rates of solutions to Euler equations with time-dependent damping ⋮ Global existence and long-time behavior of solutions to the full compressible Euler equations with damping and heat conduction in \(\mathbb{R}^3\) ⋮ $L^1$-Convergence to Generalized Barenblatt Solution for Compressible Euler Equations with Time-Dependent Damping ⋮ Global stability to steady supersonic solutions of the 1-D compressible Euler equations with frictions ⋮ High friction limit for Euler-Korteweg and Navier-Stokes-Korteweg models via relative entropy approach ⋮ Global Cauchy Problem of a System of Parabolic Conservation Laws Arising From a Keller--Segel Type Chemotaxis Model ⋮ Existence and large time behaviour of finite points blow-up solutions of the fast diffusion equation ⋮ Singularity formation for compressible Euler equations with time-dependent damping ⋮ Global and blow-up solutions for compressible Euler equations with time-dependent damping ⋮ Uniqueness and time oscillating behaviour of finite points blow-up solutions of the fast diffusion equation ⋮ Global Existence of Smooth Solutions and Convergence to Barenblatt Solutions for the Physical Vacuum Free Boundary Problem of Compressible Euler Equations with Damping ⋮ Optimal \(L^p\)-\(L^q\)-type decay rates of solutions to the three-dimensional nonisentropic compressible Euler equations with relaxation ⋮ \(L^2\)-convergence to nonlinear diffusion waves for Euler equations with time-dependent damping ⋮ The isothermal limit for the compressible Euler equations with damping ⋮ A Multiscale Meshfree Method for Macroscopic Approximations of Interacting Particle Systems ⋮ Optimal decay rates of the compressible Euler equations with time-dependent damping in \(\mathbb{R}^n\). I: Under-damping case ⋮ On global smooth solutions of the 3D spherically symmetric Euler equations with time-dependent damping and physical vacuum ⋮ Time decay of solutions to the compressible Euler equations with damping ⋮ Time-asymptotics of physical vacuum free boundaries for compressible inviscid flows with damping ⋮ Vacuum and singularity formation problem for compressible Euler equations with general pressure law and time-dependent damping ⋮ Asymptotic Behavior of Solutions Toward a Multiwave Pattern to the Cauchy Problem for the Scalar Conservation Law with the Ostwald--de Waele-Type Viscosity ⋮ Convergence to nonlinear diffusion waves for solutions of \(M_1\) model

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Convergence rates to nonlinear diffusion waves for weak entropy solutions to \(p\)-system with damping
• Domaines invariants pour les systèmes hyperboliques de lois de conservation. (Invariant domains for hyperbolic systems of the conservation law)
• Convergence of the fractional step Lax-Friedrichs scheme and Godunov scheme for the isentropic system of gas dynamics
• Asymptotic stability of a decaying solution to the Keller-Segel system of degenerate type.
• The one-dimensional Darcy's law as the limit of a compressible Euler flow
• Convergence of the viscosity method for isentropic gas dynamics
• Large time behavior of Euler-Poisson system for semiconductor
• Convergence to nonlinear diffusion waves for solutions of a system of hyperbolic conservation laws with damping
• Source-type solutions for equations of nonstationary filtration
• Uniqueness of solutions of the initial-value problem for \(u_t- \Delta\varphi (u)=0\)
• Divergence-measure fields and hyperbolic conservation laws
• Boundary effect on asymptotic behaviour of solutions to the \(p\)-system with linear damping
• Nonlinear diffusive phenomena of nonlinear hyperbolic systems
• Kinetic formulation of the isentropic gas dynamics and \(p\)-systems
• Convergence of the viscosity solutions for the system of nonlinear elasticity
• Compressible Euler equations with vacuum
• Convergence rate for compressible Euler equations with damping and vacuum
• Hyperbolic to parabolic relaxation theory for quasilinear first order systems
• Kinetic formulation for systems of two conservation laws and elastodynamics
• Compressible flow with vacuum and physical singularity.
• Convergence to the Barenblatt solution for the compressible Euler equations with damping and vacuum
• Convergence rates to nonlinear diffusion waves for solutions of system of hyperbolic conservation laws with damping
• A system of hyperbolic conservation laws with frictional damping
• Construction and qualitative behavior of the solution of the perturbated Riemann problem for the system of one-dimensional isentropic flow with damping
• Compressible flow with damping and vacuum
• Interaction of elementary waves for compressible Euler equations with frictional damping
• \(L_p\)-convergence rate to nonlinear diffusion waves for \(p\)-system with damping
• Asymptotic behavior of the solutions to the damped compressible Euler equations with vacuum
• Global $BV$ Solutions for theP-System with Frictional Damping
• Initial boundary value problem for compressible Euler equations with damping
• Estimates for Conservation Laws with Little Viscosity
• The existence of a global weak solution to the non-linear waterhammer problem
• A class of similarity solutions of the nonlinear diffusion equation
• Nonlinear diffusive phenomena of entropy weak solutions for a system of quasilinear hyperbolic conservation laws with damping
• Asymptotic L^1-decay of solutions of the porous medium equation to self-similarity
• Construction and qualitative behavior of solutions for a system of nonlinear hyperbolic conservation laws with damping
• Convergence to strong nonlinear diffusion waves for solutions of \(p\)-system with damping

This page was built for publication: \(L ^1\) convergence to the Barenblatt solution for compressible Euler equations with damping