# Well-posedness of stochastic second grade fluids

## TL;DR

This paper proves the well-posedness and stability of a stochastic second grade fluid model with Navier-slip boundary conditions, involving complex stochastic and higher-order convective terms in a two-dimensional domain.

## Contribution

It introduces a rigorous mathematical analysis demonstrating well-posedness and stability for a novel stochastic second grade fluid model with specific boundary conditions.

## Key findings

- Proved well-posedness of the stochastic second grade fluid model.
- Established stability results for the model.
- Handled complex stochastic and third-order convective terms.

## Abstract

The theory of turbulent Newtonian fluids turns out that the choice of the boundary condition is a relevant issue, since it can modify the behavior of the fluid by creating or avoiding a strong boundary layer. In this work we study stochastic second grade fluids filling a two-dimensional bounded domain, with the Navier-slip boundary condition (with friction). We prove the well-posedness of this problem and establish a stability result. Our stochastic model involves a multiplicative white noise and a convective term with third order derivatives, which significantly complicate the analysis.