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Kinetic Fokker-Planck and Landau equations with specular reflection boundary condition

H. Dong’s research is supported in part by the Simons Foundation, grant no. 709545, a Simons fellowship, grant no. 007638, and the NSF under agreement DMS-2055244.
Y. Guo's research is supported in part by NSF DMS-grant 2106650

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  • We establish existence of finite energy weak solutions to the kinetic Fokker-Planck equation and the linear 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 of [7], we prove regularity in the kinetic Sobolev spaces $ S_p $ and anisotropic Hölder spaces for such weak solutions. Such $ S_p $ regularity leads to the uniqueness of weak solutions.

    Mathematics Subject Classification: Primary: 35Q84, 35K70, 35H10, 35B45, 34A12; Secondary: 35Q70.


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