Global existence of weak solutions to two dimensional compressible viscoelastic flows

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review

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Original languageEnglish
Pages (from-to)3130-3167
Journal / PublicationJournal of Differential Equations
Issue number7
Online published4 May 2018
Publication statusPublished - 5 Oct 2018


The global existence of weak solutions of the compressible viscoelastic flows in two spatial dimensions is studied in this paper. We show the global existence if the initial velocity u0 is small in Hη with an arbitrary η∈(0,[Formula presented]) and the perturbation of (ρ0,F0) around the constant state (1,I) are small in L2∩B˙p,1 [Formula presented] with p∈([Formula presented],4). One of the main ingredients is that the velocity and the “effective viscous flux” Gi are sufficiently regular for positive time. The regularity of Gi helps to obtain the L estimate of density and deformation gradient, and hence eliminates the possible concentration and oscillation issues.

Research Area(s)

  • Compressible viscoelastic fluid, Effective viscous flux, Global well-posedness, Weak solution