Probabilistic analysis of singularities for the 3-D Navier-Stokes equations
Statistically stationary solutions to the 3-D Navier-Stokes equation do not show singularities.
Lototsky-Schnabl Operators Associated with a Strictly Elliptic Differential Operator and Their Corresponding Feller Semigroup.
Probabilistic analysis of singularities for the 3D Navier-Stokes equations
The classical result on singularities for the 3D Navier-Stokes equations says that the -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 , 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 non degenerate...
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