Electro-rheological fluids under random influences: martingale and strong solutions

2018/03/16 by Breit, Dominic, Gmeineder, Franz
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1803.06337

Abstract

We study generalised Navier--Stokes equations governing the motion of an electro-rheological fluid subject to stochastic perturbation. Stochastic effects are implemented through (i) random initial data, (ii) a forcing term in the momentum equation represented by a multiplicative white noise and (iii) a random character of the variable exponent p=p(ω,t,x) (as a result of a random electric field). We show the existence of a weak martingale solution provided the variable exponent satisfies p≥ p^->(3n)/(n+2) (p^->1 in two dimensions). Under additional assumptions we obtain also pathwise solutions.

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