Well-posedness of stochastic third grade fluid equation
Probability
2021-03-12 v1 Mathematical Physics
math.MP
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.
Cite
@article{arxiv.2103.06791,
title = {Well-posedness of stochastic third grade fluid equation},
author = {Fernanda Cipriano and Philippe Didier and Sílvia Guerra},
journal= {arXiv preprint arXiv:2103.06791},
year = {2021}
}