On stochastic evolution equations for nonlinear bipolar fluids: well-posedness and some properties of the solution

TL;DR

This paper studies stochastic evolution equations modeling nonlinear bipolar fluids with multiplicative Lévy noise, proving existence, uniqueness, and convergence of solutions using Galerkin approximation.

Contribution

It establishes the well-posedness of stochastic equations for nonlinear bipolar fluids driven by Lévy noise, a novel result in this context.

Findings

Existence of a global strong solution

Uniqueness of the solution

Convergence of Galerkin approximations in mean square

Abstract

We investigate the stochastic evolution equations describing the motion of a Non-Newtonian fluids excited by multiplicative noise of L\'evy type. By making use of Galerkin approximation we can prove that the system has a global (probabilistic) strong solution. This solution is unique and we also prove that the sequence of Galerkin solution converges to this unique solution in mean square.