This paper concerns the Cauchy problem in Rd for the stochastic Navier–Stokes equation
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∂tu=Δu−(u,∇)u−∇p+f(u)+[(σ,∇)u−∇p̃+g(u)]○Ẇ,u(0)=u0, div u=0,
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driven by white noise Ẇ. Under minimal assumptions on regularity of the coefficients and random forces, the existence of a global weak (martingale) solution of the stochastic Navier–Stokes equation is proved. In the two-dimensional case, the existence and pathwise uniqueness of a global strong solution is shown. A Wiener chaos-based criterion for the existence and uniqueness of a strong global solution of the Navier–Stokes equations is established.
Publié le : 2005-01-14
Classification:
Stochastic,
Navier–Stokes,
Leray solution,
Kraichnan’s turbulence,
Wiener chaos,
strong solutions,
pathwise uniqueness,
60H15,
35R60,
76M35
@article{1108141723,
author = {Mikulevicius, R. and Rozovskii, B. L.},
title = {Global L<sub>2</sub>-solutions of stochastic Navier--Stokes equations},
journal = {Ann. Probab.},
volume = {33},
number = {1},
year = {2005},
pages = { 137-176},
language = {en},
url = {http://dml.mathdoc.fr/item/1108141723}
}
Mikulevicius, R.; Rozovskii, B. L. Global L2-solutions of stochastic Navier–Stokes equations. Ann. Probab., Tome 33 (2005) no. 1, pp. 137-176. http://gdmltest.u-ga.fr/item/1108141723/