Advances in Differential Equations

Strong pathwise solutions of the stochastic Navier-Stokes system

Nathan Glatt-Holtz and Mohammed Ziane

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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.

Article information

Source
Adv. Differential Equations Volume 14, Number 5/6 (2009), 567-600.

Dates
First available in Project Euclid: 18 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.ade/1355867260

Mathematical Reviews number (MathSciNet)
MR2502705

Zentralblatt MATH identifier
1195.60090

Subjects
Primary: 60H15: Stochastic partial differential equations [See also 35R60] 35Q30: Navier-Stokes equations [See also 76D05, 76D07, 76N10] 76D03: Existence, uniqueness, and regularity theory [See also 35Q30]

Citation

Glatt-Holtz, Nathan; Ziane, Mohammed. Strong pathwise solutions of the stochastic Navier-Stokes system. Adv. Differential Equations 14 (2009), no. 5/6, 567--600. https://projecteuclid.org/euclid.ade/1355867260.


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