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

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 add...

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Bibliographic Details
Published in:Stochastic partial differential equations : analysis and computations 2024-09, Vol.12 (3), p.1699-1744
Main Authors: Tahraoui, Yassine, Cipriano, Fernanda
Format: Article
Language:English
Subjects:
Boundary conditions
Computational Mathematics and Numerical Analysis
Computational Science and Engineering
Mathematics
Mathematics and Statistics
Newtonian fluids
Non Newtonian fluids
Numerical Analysis
Partial Differential Equations
Probability Theory and Stochastic Processes
Sobolev space
Statistical Theory and Methods
Stochastic processes
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Summary: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 H 3 . 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.
ISSN:2194-0401
2194-041X
DOI:10.1007/s40072-023-00314-9