On the Existence and long time behaviour of H¹-Weak Solutions for 2, 3d-Stochastic 3^rd-Grade Fluids Equations

2023/11/24 by Nouira, Raya, Cipriano, Fernanda, Tahraoui, Yassine
#60H15 #76A05 #76D03 #76M35 #93D20 #Analysis of PDEs (math.AP) #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2311.14596

Abstract

In the present work, we investigate stochastic third grade fluids equations in a d-dimensional setting, for d = 2, 3. More precisely, on a bounded and simply connected domain D of ℝ^d, d = 2,3, with a sufficiently regular boundary ∂ D, we consider incompressible third grade fluid equations perturbed by a multiplicative Wiener noise. Supplementing our equations by Dirichlet boundary conditions and taking initial data in the Sobolev space H¹(D), we establish the existence of global stochastic weak solutions by performing a strategy based on the conjugation of stochastic compactness criteria and monotonicity techniques. Furthermore, we study the asymptotic behaviour of these solutions, as t → ∞.

Related

• On the existence and long time behaviour of H1-weak solutions for 2, 3d-stochastic 3rd-grade fluids equations
• Well-posedness of stochastic third grade fluid equation
• A note on stochastic Navier-Stokes equations with not regular multiplicative noise
• Strong solutions for a stochastic model of 2-D second grade fluids driven by Lévy noise
• Anticipating stochastic equation of two-dimensional second grade fluids