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arXiv · 1409.0803

On the Smoluchowski-Kramers approximation for a system with infinite degrees of freedom exposed to a magnetic field

Sandra Cerrai·Michael Salins
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Abstract

We study the validity of the so-called Smoluchowski-Kramers approximation for a two dimensional system of stochastic partial differential equations, subject to a constant magnetic field. As the small mass limit does not yield to the solution of the corresponding first order system, we regularize our problem by adding a small friction. We show that in this case the Smoluchowski-Kramers approximation holds. We also give a justification of the regularization, by showing that the regularized problems provide a good approximation to the original ones.

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Sandra Cerrai, Michael Salins. 2014-09-02. On the Smoluchowski-Kramers approximation for a system with infinite degrees of freedom exposed to a magnetic field. https://arxiv.org/abs/1409.0803

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