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Stochastic power law fluids: Existence and uniqueness of weak solutions

Yutaka Terasawa, Nobuo Yoshida

Published 2010-02-07, updated 2012-01-04Version 3

We consider a stochastic partial differential equation (SPDE) which describes the velocity field of a viscous, incompressible non-Newtonian fluid subject to a random force. Here the extra stress tensor of the fluid is given by a polynomial of degree $p-1$ of the rate of strain tensor, while the colored noise is considered as a random force. We investigate the existence and the uniqueness of weak solutions to this SPDE.

Comments: Published in at http://dx.doi.org/10.1214/10-AAP741 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)
Journal: Annals of Applied Probability 2011, Vol. 21, No. 5, 1827-1859
Categories: math.PR
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