Analyticity of solutions for randomly forced two-dimensional Navier-Stokes equations

A. Shirikyan

Research output: Contribution to journalArticle

12 Citations (Scopus)

Abstract

A study is made of randomly forced two-dimensional Navier-Stokes equations with periodic boundary conditions. Under the assumption that the random forcing is analytic in the spatial variables and is a white noise in the time, it is proved that a large class of solutions, which contains all stationary solutions with finite energy, admits analytic continuation to a small complex neighbourhood of the torus. Moreover, a lower bound is obtained for the radius of analyticity in terms of the viscosity v, and it is shown that the Kolmogorov dissipation scale can be asymptotically estimated below by v2+d for any d > 0.

Original languageEnglish
Pages (from-to)785-799
Number of pages15
JournalUspekhi Matematicheskikh Nauk
Volume57
Issue number4
DOIs
Publication statusPublished - Jul 2002

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