Well-posedness of stochastic third grade fluid equation

TL;DR

This paper proves the existence and uniqueness of solutions for a stochastic third grade fluid equation with multiplicative noise, modeling non-Newtonian fluid flow with viscoelastic properties in bounded domains.

Contribution

It establishes the well-posedness of a complex nonlinear stochastic PDE describing non-Newtonian fluids with viscoelastic features, including boundary conditions.

Findings

Existence of strong solutions in 2D domains.

Uniqueness of solutions under given conditions.

Handling of multiplicative white noise perturbations.

Abstract

In this paper, we establish the well-posedness for the third grade fluid equation perturbed by a multiplicative white noise. This equation describes the motion of a non-Newtonian fluid of differential type with relevant viscoelastic properties. We are faced with a strongly nonlinear stochastic partial differential equation supplemented with a Navier slip boundary condition. Taking the initial condition in the Sobolev space H^2, we show the existence and the uniqueness of the strong (in the probability sense) solution in a two dimensional and non axisymmetric bounded domain.