• Corpus ID: 17044797

Strong pathwise solutions of the stochastic Navier-Stokes system

  title={Strong pathwise solutions of the stochastic Navier-Stokes system},
  author={Nathan Glatt-Holtz and Mohammed Ziane},
  journal={Advances in Differential Equations},
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. 
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