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Two-Dimensional Navier–Stokes Equations Driven by a Space–Time White Noise

✍ Scribed by Giuseppe Da Prato; Arnaud Debussche

Publisher: Elsevier Science
Year: 2002
Tongue: English
Weight: 247 KB
Volume: 196
Category: Article
ISSN: 0022-1236
DOI: 10.1006/jfan.2002.3919

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✦ Synopsis

We study the two-dimensional Navier-Stokes equations with periodic boundary conditions perturbed by a space-time white noise. It is shown that, although the solution is not expected to be smooth, the nonlinear term can be defined without changing the equation. We first construct a stationary martingale solution.Then, we prove that, for almost every initial data with respect to a measure supported by negative spaces, there exists a unique global solution in the strong probabilistic sense.

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