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Global well‐posedness for the stochastic non‐Newtonian fluid equations and convergence to the Navier‐Stokes equations
Author(s) -
Henandez Marco,
Nguyen Phuong
Publication year - 2020
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.6827
Subject(s) - mathematics , martingale (probability theory) , navier–stokes equations , mathematical analysis , compressibility , convergence (economics) , limit (mathematics) , weak solution , galerkin method , newtonian fluid , hagen–poiseuille flow from the navier–stokes equations , nonlinear system , classical mechanics , physics , quantum mechanics , economics , economic growth , thermodynamics
We establish the existence of global pathwise solutions for the stochastic non‐Newtonian incompressible fluid equations in two space dimensions. Moreover, we show that said solutions converge in probability to solutions of the stochastic Navier‐Stokes equations in the appropriate limit. Our approach is based on Galerkin approximations and the theory of martingale solutions.