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Published on: December 4, 2017
Background Vlasov equations and Young measures for passive scalar and vector advection equations under special
Federico Butori1, Franco Flandoli1, Eliseo Luongo1,2
1Scuola Normale Superiore, Piazza dei Cavalieri, 7, 56126 Pisa, Italia.
Abstract:
In the last few years it was proved that scalar passive quantities subject to suitable stochastic transport noise, and more recently that also vector passive quantities subject to suitable stochastic transport and stretching noise, weakly converge to the solutions of deterministic equations with a diffusion term. In the background of these stochastic models, we introduce stochastic Vlasov equations which give additional information on the fluctuations and oscillations of solutions: we prove convergence to non-trivial Young measures satisfying limit PDEs with suitable diffusion terms. In the case of a passive vector field the background Vlasov equation adds completely new statistical information to the stochastic advection equation.
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