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math.AP2023
Gradient Decay in the Boltzmann theory of Non-isothermal boundary
Hongxu Chen, Chanwoo Kim
We consider the Boltzmann equation in convex domain with non-isothermal boundary of diffuse reflection. For both unsteady/steady problems, we construct solutions belong to $W^{1,p}…
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…