Displaying similar documents to “Note on the internal stabilization of stochastic parabolic equations with linearly multiplicative gaussian noise”

Probabilistic analysis of singularities for the 3D Navier-Stokes equations

Franco Flandoli, Marco Romito (2002)

Mathematica Bohemica

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The classical result on singularities for the 3D Navier-Stokes equations says that the 1 -dimensional Hausdorff measure of the set of singular points is zero. For a stochastic version of the equation, new results are proved. For statistically stationary solutions, at any given time t , with probability one the set of singular points is empty. The same result is true for a.e. initial condition with respect to a measure related to the stationary solution, and if the noise is sufficiently...

Local Solutions for Stochastic Navier Stokes Equations

Alain Bensoussan, Jens Frehse (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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In this article we consider local solutions for stochastic Navier Stokes equations, based on the approach of Von Wahl, for the deterministic case. We present several approaches of the concept, depending on the smoothness available. When smoothness is available, we can in someway reduce the stochastic equation to a deterministic one with a random parameter. In the general case, we mimic the concept of local solution for stochastic differential equations.