The 2-$D$ constrained $NS$ equation and stochastic vortex theory

The 2-$D$ constrained $NS$ equation and stochastic vortex theory

We consider a modified version of the two-dimensional NS equation introduced in [4], [5] preserving energy and momentum of inertia. The physical motivation of this approach is the occurrence of di¤erent dissipation time scales. The constraint we consider is related to the gradient flow structure of...

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Veröffentlicht in:Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni 2012-01, Vol.23 (1), p.1-27
Hauptverfasser: Pulvirenti, Mario, Rossi, E
Format: Artikel
Sprache:eng
Schlagworte:
Inertia (Mechanics)
Mathematical research
Navier-Stokes equations
Partial differential equations
Probability theory and stochastic processes
Vortex motion
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Zusammenfassung:We consider a modified version of the two-dimensional NS equation introduced in [4], [5] preserving energy and momentum of inertia. The physical motivation of this approach is the occurrence of di¤erent dissipation time scales. The constraint we consider is related to the gradient flow structure of the 2-D Navier-Stokes equation with respect to the Wasserstein metric. In this paper we justify the choice of this metric from the point of view of the stochastic vortex theory.
ISSN:1120-6330
1720-0768
DOI:10.4171/RLM/614