Abstract: We investigate the stochastic equation for the motion of a second grade fluid filling a bounded (or periodic) domain of R2. Global existence of probabilistic weak solutions (and weak in the sense of partial differential equations) is expounded. We are also able to prove the pathwise uniqueness of solution. The two results yield the unique existence of probabilistic strong solution. On this basis we show that under suitable conditions on the data we can construct a sequence of solutions of the stochastic second grade fluid that converges to the probabilistic weak solution of the stochastic Navier-Stokes equations when the physical parameter α tends to zero. This is a joint work with Prof Mamadou Sango (Department of Mathematics and Applied Mathematics, University of Pretoria).
Some mathematical problems in the dynamics of stochastic second-grade fluids
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