Méthodes de couplage pour des équations stochastiques de type Navier-Stokes et Schrödinger

Abstract : In a first part, we are concerned with stochastic two-dimensional Navier-Stokes (NS), non-linear Schrödinger (NLS) and Complex Ginzburg-Landau
(CGL) equations driven by a noise which is white in time and smooth in space. Using coupling arguments, we establish exponential (resp polynomial) mixing of
NS and CGL (resp NLS) provided the noise is non degenerate on the low modes. Although, this kind of method was originally developed for strongly dissipative
equations with additive noise, we are able to treat non dissipative equation (NLS) and general non additive noise.
In a second part, we are concerned with stochastic three-dimensional Navier-Stokes equations (NS3D). We first investigate smoothness properties in space of
the stationary solutions. Some informations on the Kolmogorov dissipation scale (K41) are deduced. Then we establish exponential mixing of the solutions of NS3D
provided the noise is at the same time sufficiently smooth and non degenerate.
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Submitted on : Thursday, December 15, 2005 - 5:48:40 PM
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Cyril Odasso. Méthodes de couplage pour des équations stochastiques de type Navier-Stokes et Schrödinger. Mathématiques [math]. Université Rennes 1, 2005. Français. ⟨tel-00011214⟩

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