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Kinetic Fokker-Planck and Landau Equations with Specular Reflection Boundary Condition (2111.09840v1)
Published 18 Nov 2021 in math.AP
Abstract: We establish existence of finite energy weak solutions to the kinetic Fokker-Planck equation and the linearized Landau equation near Maxwellian, in the presence of specular reflection boundary condition for general domains. Moreover, by using a method of reflection and the $S_p$ estimate previously established by the first and the last author, we prove regularity in the kinetic Sobolev spaces $S_p$ and anisotropic H\"older spaces for such weak solutions. Such $S_p$ regularity leads to the uniqueness of weak solutions.