On the existence and long time behaviour of H1-weak solutions for 2, 3d-stochastic 3rd-grade fluids equations

2026/06/09 by Raya Nouira, Fernanda Cipriano, Yassine Tahraoui
Computer Science · Economics, Econometrics and Finance · Mathematics · #Advanced Mathematical Modeling in Engineering #Nonlinear Partial Differential Equations #Stochastic processes and financial applications

paper · doi:10.1016/j.na.2026.114197

openalex created_date 2023/11/28 · openalex publication_date 2026/06/09 · openalex updated_date 2026/07/28

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 → ∞.

Citations

• Well-posedness of stochastic third grade fluid equation
• Martingale solutions for the three-dimensional stochastic nonhomogeneous incompressible Navier-Stokes equations driven by Levy processes
• Optimal control for two-dimensional stochastic second grade fluids
• Existence of a martingale solution of the stochastic Navier-Stokes\n equations in unbounded 2D and 3D-domains

Related

• On the Existence and long time behaviour of H¹-Weak Solutions for 2, 3d-Stochastic 3^rd-Grade Fluids Equations
• Well-posedness of stochastic third grade fluid equation
• Anticipating stochastic equation of two-dimensional second grade fluids
• A note on stochastic Navier-Stokes equations with not regular\n multiplicative noise
• Strong solutions for a stochastic model of 2-D second grade fluids driven by Lévy noise