Abstract
We consider the stochastic Navier-Stokes equations forced by a multiplicative white noise on a bounded domain in space dimensions two and three. We establish the local existence and uniqueness of strong or pathwise solutions when the initial data takes values in $H^1$. In the two-dimensional case, we show that these solutions exist for all time. The proof is based on finite-dimensional approximations, decomposition into high and low modes and pairwise comparison techniques.
Citation
Nathan Glatt-Holtz. Mohammed Ziane. "Strong pathwise solutions of the stochastic Navier-Stokes system." Adv. Differential Equations 14 (5/6) 567 - 600, May/June 2009. https://doi.org/10.57262/ade/1355867260
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