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Abstract
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We derive the hydrodynamic limit of a kinetic equation where the interactions in
velocity are modeled by a linear operator (Fokker–Planck or linear Boltzmann) and
the force in the Vlasov term is a stochastic process with high amplitude and
short-range correlation. In the scales and the regime we consider, the hydrodynamic
equation is a scalar second-order stochastic partial differential equation.
Compared to the deterministic case, we also observe a phenomenon of enhanced
diffusion.
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Keywords
diffusion-approximation, kinetic equation, hydrodynamic
limit
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Mathematical Subject Classification 2010
Primary: 35Q20, 35R60, 60H15, 35B40
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Milestones
Received: 15 March 2019
Accepted: 16 November 2019
Published: 20 May 2020
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