Well-posedness of stochastic third grade fluid equation

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In this paper, we establish the well-posedness for the third grade fluid equation perturbed by a multiplicative white noise. This equation describes the motion of a non-Newtonian fluid of differential type with relevant viscoelastic properties. We are faced with a strongly nonlinear stochastic partial differential equation supplemented with a Navier slip boundary condition. Taking the initial condition in the Sobolev space H2, we show the existence and the uniqueness of the strong (in the probability sense) solution in a two dimensional and non axisymmetric bounded domain.

Original languageEnglish
Pages (from-to)496-535
Number of pages40
JournalJournal Of Differential Equations
Publication statusPublished - 5 Jun 2021


  • Non-Newtonian fluid
  • Stochastic partial differential equation
  • Third grade fluid
  • Well-posedness


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