On the convergence of the two-dimensional second grade fluid model to the Navier-Stokes equation

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Abstract

We consider the equations governing the motion of incompressible second grade fluids in a bounded two-dimensional domain with Navier-slip boundary conditions. We first prove that the corresponding solutions are uniformly bounded with respect to the normal stress modulus α in the L-H1 and the L2-H2 time-space norms. Next, we study their asymptotic behavior when α tends to zero, prove that they converge to regular solutions of the Navier-Stokes equations and give the rate of convergence in terms of α.

Original languageEnglish
Pages (from-to)2557-2586
Number of pages30
JournalJournal Of Differential Equations
Volume260
Issue number3
DOIs
Publication statusPublished - 5 Feb 2016

Keywords

  • Navier-slip boundary conditions
  • Navier-Stokes equations
  • Rate of convergence
  • Second grade fluids
  • Uniform a priori estimates

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