Malliavin Calculus for the Stochastic 2D Navier Stokes Equation

Simple item page
dc.creatorMattingly, Jonathan C.
dc.creatorPardoux, Etienne
dc.date2004-07-13
dc.date2005-10-12
dc.date.accessioned2026-07-07T06:38:39Z
dc.date.available2026-07-07T06:38:39Z
dc.descriptionWe consider the incompressible, two dimensional Navier Stokes equation with periodic boundary conditions under the effect of an additive, white in time, stochastic forcing. Under mild restrictions on the geometry of the scales forced, we show that any finite dimensional projection of the solution possesses a smooth density with respect to Lebesgue measure. We also show that under natural assumptions the density of such a projection is everywhere strictly positive. In particular, our conditions are viscosity independent. We are mainly interested in forcing which excites a very small number of modes. All of the results rely on the nondegeneracy of the infinite dimensional Malliavin matrix.
dc.description42 Pages. Corrected version. Fixed error in the simple existence lemma (The smoothness proof still also gave existence.) Fixed sign and power typo in two equations and the formulation of equation(for clarity)
dc.identifierhttps://arxiv.org/abs/math/0407215
dc.identifierhttp://arxiv.org/abs/math/0407215
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/100813
dc.subjectProbability
dc.subjectMathematical Physics
dc.subjectAnalysis of PDEs
dc.subjectDynamical Systems
dc.subject60H15; 60H30; 60H07; 76F20; 76B03; 35J60
dc.titleMalliavin Calculus for the Stochastic 2D Navier Stokes Equation
dc.typetext

Files

Collections

arXiv