| Abstract: |
| In this talk we discuss the existence of solutions of a Smagorinsky - Ladyzhenskaya equation from fluid mechanics driven by a Levy noise following an article to appear by the authors. The deterministic part of the equation corresponds to a version of the Navier Stokes equations with the Laplacian replaced by the nonlinear Laplacian. This equation has been proposed as a model of turbulence in atmospheric sciences by Smagorinsky, and it has been proposed by Ladyzhenskaya as a way to overcome the difficulties related to the 3D Navier Stokes equations. The Levy noise is added to this equation. We aim to show the existence of martingale and pathwise solutions to this stochastic pde.
One of the difficulties to overcome is the proof of compactness of approximations, which is hampered by the fact that the natural Galerkin projectors are not projectors in the L^2 and dual spaces. |
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