Local strong solutions to the stochastic third grade fluid equations with Navier boundary conditions

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Abstract

This work is devoted to the study of non-Newtonian fluids of grade three on two-dimensional and three-dimensional bounded domains, driven by a nonlinear multiplicative Wiener noise. More precisely, we establish the existence and uniqueness of the local (in time) solution, which corresponds to an addapted stochastic process with sample paths defined up to a certain positive stopping time, with values in the Sobolev space H3 . Our approach combines a cut-off approximation scheme, a stochastic compactness arguments and a general version of Yamada–Watanabe theorem. This leads to the existence of a local strong pathwise solution.
Original languageEnglish
Pages (from-to)1699–1744
Number of pages46
JournalStochastics and Partial Differential Equations: Analysis and Computations
Volume12
Early online date9 Oct 2023
DOIs
Publication statusPublished - Sept 2024

Keywords

  • Navier-slip boundary conditions
  • Stochastic PDE
  • Third grade fluids
  • Well-posedness

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