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May/June 2009 Strong pathwise solutions of the stochastic Navier-Stokes system
Nathan Glatt-Holtz, Mohammed Ziane
Adv. Differential Equations 14(5/6): 567-600 (May/June 2009).

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

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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.

Information

Published: May/June 2009
First available in Project Euclid: 18 December 2012

zbMATH: 1195.60090
MathSciNet: MR2502705

Subjects:
Primary: 35Q30, 60H15, 76D03

Rights: Copyright © 2009 Khayyam Publishing, Inc.

JOURNAL ARTICLE
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Vol.14 • No. 5/6 • May/June 2009
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