Malliavin calculus for the stochastic 2D Navier-Stokes equation
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We 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, strictly positive density with respect to Lebesgue measure. In particular, our conditions are viscosity independent. We are mainly interested in forcing that excites a very small number of modes. All of the results rely on proving the nondegeneracy of the infinite-dimensional Malliavin matrix. © 2006 Wiley Periodicals, Inc.
Published Version (Please cite this version)10.1002/cpa.20136
Publication InfoMattingly, Jonathan Christopher; & Pardoux, E (2006). Malliavin calculus for the stochastic 2D Navier-Stokes equation. Communications on Pure and Applied Mathematics, 59(12). pp. 1742-1790. 10.1002/cpa.20136. Retrieved from http://hdl.handle.net/10161/15778.
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Professor of Mathematics
Jonathan Christopher Mattingly grew up in Charlotte, NC where he attended Irwin Ave elementary and Charlotte Country Day. He graduated from the NC School of Science and Mathematics and received a BS is Applied Mathematics with a concentration in physics from Yale University. After two years abroad with a year spent at ENS Lyon studying nonlinear and statistical physics on a Rotary Fellowship, he returned to the US to attend Princeton University where he obtained a PhD in Applied and