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math.AP2023
Boundary effect under 2D Newtonian gravity potential in the phase space
Jiaxin Jin, Chanwoo Kim
We study linear two-half dimensional Vlasov equations under the logarithmic gravity potential in the half space of diffuse reflection boundary. We prove decay-in-time of the expone…
math.AP2023
Asymptotics of Helmholtz-Kirchhoff Point-Vortices in the Phase Space
Chanwoo Kim, Trinh T. Nguyen
A rigorous derivation of point vortex systems from kinetic equations has been a challenging open problem, due to singular layers in the inviscid limit, giving a large velocity grad…
math.AP2022
Exponential Mixing of Vlasov equations under the effect of Gravity and Boundary
Jiaxin Jin, Chanwoo Kim
In this paper, we study exponentially fast mixing induced/enhanced by gravity and stochastic boundary in the kinetic theory of Vlasov equations. We consider the Vlasov equations wi…