Some examples of absolute continuity of measures in stochastic fluid dynamics

Details Some examples of absolute continuity of measures in stochastic fluid dynamics Some examples of absolute continuity of measures in stochastic fluid dynamics

2008-01-03

arxiv.org/abs/0801.0496v1

Mathematics

Probability

16 pages

Scientific paper

A non linear Ito equation in a Hilbert space is studied by means of Girsanov theorem. We consider a non linearity of polynomial growth in suitable norms, including that of quadratic type which appears in the Kuramoto-Sivashinsky equation and in the Navier-Stokes equation. We prove that Girsanov theorem holds for the 1-dimensional stochastic Kuramoto-Sivashinsky equation and for a modification of the 2- and 3-dimensional stochastic Navier-Stokes equation. In this way, we prove existence and uniqueness of solutions for these stochastic equations. Moreover, the asymptotic behaviour for large time is characterized.

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