Qualitative properties of stationary measures for three-dimensional Navier-Stokes equations
The non-stationary, three-dimensional Navier-Stokes equation is considered. It is assumed that the exterior force which appears in the right-hand side of Navier-Stokes equation is the time derivative of a random process with independent increments and sufficiently non-degenerate distribution in the space variables. The purpose of this paper is to study the distribution of stationary solutions of Navier-Stokes equation for the right-hand side described above. It is proved 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.
scientific article; zbMATH DE number 5190785
scientific article