Conservation of Total Vorticity for a 2D Stochastic Navier Stokes Equation

Peter M. Kotelenez and Bradley T. Seadler

Advances in Mathematical Physics, 2011, vol. 2011, issue 1

Abstract: We consider N point vortices whose positions satisfy a stochastic ordinary differential equation on ℝ2N perturbed by spatially correlated Brownian noise. The associated signed point measure‐valued empirical process turns out to be a weak solution to a stochastic Navier‐Stokes equation (SNSE) with a state‐dependent stochastic term. As the number of vortices tends to infinity, we obtain a smooth solution to the SNSE, and we prove the conservation of total vorticity in this continuum limit.

Date: 2011
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https://doi.org/10.1155/2011/862186

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlamp:v:2011:y:2011:i:1:n:862186

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