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, 1-14

Abstract:

We consider ð ‘ point vortices whose positions satisfy a stochastic ordinary differential equation on â„ 2 ð ‘ 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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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlamp:862186

DOI: 10.1155/2011/862186

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