Long-time behavior and weak-strong uniqueness for incompressible viscoelastic flows

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

15 Scopus Citations
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Detail(s)

Original languageEnglish
Pages (from-to)3437-3461
Journal / PublicationDiscrete and Continuous Dynamical Systems- Series A
Volume35
Issue number8
Publication statusPublished - Aug 2015

Abstract

We consider the Cauchy problem for incompressible viscoelastic uids in the whole space Rd (d = 2, 3). By introducing a new decomposition via Helmholtz's projections, we first provide an alternative proof on the existence of global smooth solutions near equilibrium. Then under additional assumptions that the initial data belong to L1 and their Fourier modes do not degenerate at low frequencies, we obtain the optimal L2 decay rates for the global smooth solutions and their spatial derivatives. At last, we establish the weak-strong uniqueness property in the class of finite energy weak solutions for the incompressible viscoelastic system.

Research Area(s)

  • Long-time behavior, Navier-Stokes equations, Optimal decay rate, Viscoelastic flow, Weak-strong uniqueness