Strong pathwise solutions of the stochastic Navier-Stokes system
By Nathan E. Glatt-Holtz, Mohammed B. Ziane. Advances in Differential Equations, 2009
174 citations recorded by the source corpus.
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.
Subfields: Computational Theory and Mathematics, Control and Systems Engineering, Finance
View Paper: https://www.semanticscholar.org/paper/2dc68522bb857714ee1cd56fe72142b83169ab7c
How researchers see this paper
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In Computational Theory and Mathematics
In Control and Systems Engineering
In Finance
- Roger Temam
- Nathan E. Glatt-Holtz
- Arnaud Debussche
- Martina Hofmanov'a
- Martin Hairer
- Xiangchan Zhu
- Rongchan Zhu
- Panagiotis E. Souganidis
Citations in the corpus
- Parameter estimation for the stochastically perturbed Navier-Stokes equations (2010, unknown): “See, for instance, [2, 3, 4, 7, 12, 13, 30] and containing references.”
- Local martingale and pathwise solutions for an abstract fluids model (2010, methodology): “In any case the work here provides an alternative proof of the results in [20].”