Weak solution for 3D-stochastic third grade fluid equations

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Abstract

This article studies the stochastic evolution of incompressible non-Newtonian fluids of differential type. More precisely, we consider the equations governing the dynamic of a third grade fluid filling a three-dimensional bounded domain O, perturbed by a multiplicative white noise. Taking the initial condition in the Sobolev space H2 (O), and supplementing the equations with a Navier slip boundary condition, we establish the existence of a global weak stochastic solution with sample paths in L (0, T; H2 (O)).

Original languageEnglish
Article number3211
Pages (from-to)1-16
Number of pages16
JournalWater (Switzerland)
Volume12
Issue number11
DOIs
Publication statusPublished - 16 Nov 2020

Keywords

  • Non-Newtonian fluid
  • Stochastic partial differential equation
  • Third grade fluid
  • Turbulent flow

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