- 06-215 Armen Shirikyan
- Qualitative properties of stationary measures for three-dimensional Navier-Stokes equations
Aug 2, 06
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Abstract. The paper is devoted to studying the distribution of stationary solutions for 3D Navier-Stokes equations perturbed by a random force. Under a non-degeneracy assumption, we show that the support of such a distribution coincides with the entire phase space, and its finite-dimensional projections are minorised by a measure possessing an almost surely positive smooth density with respect to the Lebesgue measure. Similar assertions are true for weak solutions of the Cauchy problem with a regular initial function.