Global existence of weak solutions to two dimensional compressible viscoelastic flows
type: Item
instance of: scholarly article
title: Global existence of weak solutions to two dimensional compressible viscoelastic flows
zbMATH Open document ID: 1394.35360
author: Xianpeng Hu
published in: Journal of Differential Equations
publication date: 2018-06-18T00:00:00Z
review text: The author studies the existence of weak solutions of the compressible viscoelastic flows in two spatial dimensions. The global existence is proved if the initial velocity is small in the Sobolev space \(H^\eta\) with an arbitrary \(\eta\in(0, 1/2)\), and the perturbation of the density and the deformation gradient around the constant state \((1;,I)\) are small in \(L^2\cap \dot B^{2/p}_{p,1}\) with suitable \(p\). The main ingredient of the proof is that the velocity and the ``effective viscous flux'' are sufficiently regular for positive time. The regularity of these fluxes helps to obtain the \(L^1\) estimate of density and deformation gradient, and hence eliminates the possible concentration and oscillation issues.
reviewed by: Piotr Biler
Mathematics Subject Classification ID: 35Q35
Mathematics Subject Classification ID: 76A10
Mathematics Subject Classification ID: 76D03
Mathematics Subject Classification ID: 35A01
Mathematics Subject Classification ID: 35D30
zbMATH DE Number: 6890653
zbMATH Keywords: compressible viscoelastic fluid
zbMATH Keywords: effective viscous flux
zbMATH Keywords: global well-posedness
MaRDI profile type: Publication
full work available at URL: j.jde.2018.05.001
OpenAlex ID: W2801022560
cites work: Fourier Analysis and Nonlinear Partial Differential Equations
cites work: Existence of global weak solutions to the kinetic Hookean dumbbell model for incompressible dilute polymeric fluids
cites work: Existence of large-data finite-energy global weak solutions to a compressible Oldroyd-B model
cites work: Global weak solutions for some Oldroyd models
cites work: Q4112938
cites work: The Global Existence of Small Solutions to the Incompressible Viscoelastic Fluid System in 2 and 3 Space Dimensions
cites work: About lifespan of regular solutions of equations related to viscoelastic fluids
cites work: Note on global regularity for two-dimensional Oldroyd-B fluids with diffusive stress
cites work: Remarks on Oldroyd-B and related complex fluid models
cites work: Q5702675
cites work: Global solutions of the Navier-Stokes equations for multidimensional compressible flow with discontinuous initial data
cites work: Strong convergence to global solutions for multidimensional flows of compressible, viscous fluids with polytropic equations of state and discontinuous initial data
cites work: Dynamics of singularity surfaces for compressible, viscous flows in two space dimensions
cites work: Global existence for the multi-dimensional compressible viscoelastic flows
cites work: Global existence and optimal decay rates for three-dimensional compressible viscoelastic flows
cites work: Global Solutions of Two-Dimensional Incompressible Viscoelastic Flows with Discontinuous Initial Data
cites work: Global solutions to repulsive Hookean elastodynamics
cites work: Global well-posedness of classical solutions with large oscillations and vacuum to the three-dimensional isentropic compressible Navier-Stokes equations
cites work: A Beale-Kato-Madja breakdown criterion for an Oldroyd-B fluid in the creeping flow regime
cites work: Global solutions for incompressible viscoelastic fluids
cites work: Almost global existence for 2-D incompressible isotropic elastodynamics
cites work: Global well-posedness of incompressible elastodynamics in two dimensions
cites work: On hydrodynamics of viscoelastic fluids
cites work: On the initial‐boundary value problem of the incompressible viscoelastic fluid system
cites work: Q4389323
cites work: Global solutions for some Oldroyd models of non-Newtonian flows
cites work: Global existence of weak solutions to the FENE dumbbell model of polymeric flows
cites work: Global existence of weak solutions to macroscopic models of polymeric flows
cites work: Global well-posedness for compressible viscoelastic fluids near equilibrium
cites work: Global existence for three‐dimensional incompressible isotropic elastodynamics via the incompressible limit
cites work: Global existence for three‐dimensional incompressible isotropic elastodynamics
cites work: Global solution to the incompressible Oldroyd-B model in the critical \(L^{p}\) framework: the case of the non-small coupling parameter
cites work: Emergence of singular structures in Oldroyd-B fluids
Wikidata QID: Q129872057
DOI: 10.1016/J.JDE.2018.05.001
description: scientific article; zbMATH DE number 6890653