On the Smoluchowski-Kramers approximation for a system with infinite degrees of freedom exposed to a magnetic field
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Citation (published version)Sandra Cerrai, Michael Salins. 2017. "On the Smoluchowski-Kramers approximation for a system with infinite degrees of freedom exposed to a magnetic field." STOCHASTIC PROCESSES AND THEIR APPLICATIONS, Volume 127, Issue 1, pp. 273 - 303 (31). https://doi.org/10.1016/j.spa.2016.06.008
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. Since 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.