Malliavin calculus for highly degenerate 2D stochastic Navier-Stokes equations
UNSPECIFIED. (2004) Malliavin calculus for highly degenerate 2D stochastic Navier-Stokes equations. COMPTES RENDUS MATHEMATIQUE, 339 (11). pp. 793-796. ISSN 1631-073XFull text not available from this repository.
Official URL: http://dx.doi.org/10.1016/j.crma.2004.09.002
This Note mainly presents the results from "Malliavin calculus and the randomly forced Navier-Stokes equation" by J.C. Mattingly and E. Pardoux. It also contains a result from ''Ergodicity of the degenerate stochastic 2D Navier-Stokes equation'' by M. Hairer and J.C. Mattingly. We study the Navier-Stokes equation on the two-dimensional torus when forced by a finite dimensional Gaussian white noise. We give conditions under which the law of the solution at any time iota > 0, projected on a finite dimensional subspace, has a smooth density with respect to Lebesgue measure. In particular. our results hold for specific choices of four dimensional Gaussian white noise. Under additional assumptions. we Show that the preceding density is everywhere strictly positive. This Note's results are a critical component in the ergodic results discussed in a future article.
|Item Type:||Journal Article|
|Subjects:||Q Science > QA Mathematics|
|Journal or Publication Title:||COMPTES RENDUS MATHEMATIQUE|
|Publisher:||EDITIONS SCIENTIFIQUES MEDICALES ELSEVIER|
|Official Date:||1 December 2004|
|Number of Pages:||4|
|Page Range:||pp. 793-796|
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