Weak vorticity formulation of 2D Euler equations with white noise initial condition

2017/07/25 by Flandoli, Franco · 1 citation
#FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1707.08068

Abstract

The 2D Euler equations with random initial condition distributed as a certain Gaussian measure are considered. The theory developed by S. Albeverio and A.-B. Cruzeiro is revisited, following the approach of weak vorticity formulation. A solution is constructed as a limit of random point vortices. This allows to prove that it is also limit of L^∞-vorticity solutions. The result is generalized to initial measures that have a continuous bounded density with respect to the original Gaussian measure.

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• Incompressible 2D Euler equations with non-decaying random initial vorticity

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