Monday, May 27, 2024 - 10:10 in ZiF, plenary hall
On stochastic third grade fluid equations with Navier boundary conditions: 2D $\&$ 3D setting
A talk in the SPDEvent series by
Yassine Tahraoui from Scuola Normale Superiore
| Abstract: |
Most studies on fluid dynamics have been devoted to Newtonian fluids, which are characterized by the classical Newton's law of viscosity (Navier-Stokes equations). However, there exist many real fluids with nonlinear viscoelastic behavior that does not obey Newton's law of viscosity e.g. toothpaste, paint, blood, melted butter, shampoo and nanofluids. My aim is to discuss the well-posedness of a class of non-Newtonian fluids of differential type (Rivlin-Ericksen fluids) in the presence of stochastic forcing. Namely, the strong local well-posedness, in PDEs and probabilistic senses, of the 2D/3D stochastic $3^{rd}$-grade fluids in the presence of multiplicative noise driven by a Wiener process. Our approach uses stochastic compactness tools with an appropriate cut-off of the system, where the Navier boundary conditions play a crucial role to get some uniform estimates.
The talk is based on a recent work [1], with Fernanda Cipriano (CMA, Univ. NOVA de Lisboa).
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