On the asymptotic behaviour and stochastic stabilization of second grade fluids

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Abstract

In this article, we study stability properties for two-dimensional non-Newtonian fluids. More precisely, we consider stochastic perturbations of the second grade fluid equations, with Navier slip boundary condition, and analyse the asymptotic behaviour of the solutions as t→+∞. We prove that the strong solutions (in the probability sense) of the stochastic evolutionary equation converge exponentially to the stationary solution in the mean square and almost surely. In addition, we study the stabilization of the deterministic model by introducing a suitable stochastic noise.

Original languageEnglish
JournalStochastics
DOIs
Publication statusPublished - 1 Jan 2019

Keywords

  • Second grade fluids
  • stability
  • stabilization
  • stochastic

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