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arXiv · 1803.06337

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

Dominic Breit·Franz Gmeineder
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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 $p=p(\omega,t,x)$ (as a result of a random electric field). We show the existence of a weak martingale solution provided the variable exponent satisfies $p\geq p^->\frac{3n}{n+2}$ ($p^->1$ in two dimensions). Under additional assumptions we obtain also pathwise solutions.

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Dominic Breit, Franz Gmeineder. 2018-03-16. Electro-rheological fluids under random influences: martingale and strong solutions. https://arxiv.org/abs/1803.06337

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