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Analysis Seminar

Thursday, February 6, 2020 - 3:00pm

Jin Woo Jang

IBS, Korea

Location

University of Pennsylvania

DRL 3C6

 In this talk, I will introduce a recent development in the global well-posedness of the kinetic Landau equation in a general smooth bounded domain. This work proves the global stability of the Landau equation in an $L^1_{x,v}$ framework with the Coulombic potential in a general smooth bounded domain with the specular reflection boundary condition for initial perturbations of the Maxwellian equilibrium states. Our methods consist of the generalization of the well-posedness theory for the Fokker-Planck equation (HJV-2014, HJJ-2018) and the extension of the boundary value problem to a whole space problem, as well as the use of a recent extension of De Giorgi-Nash-Moser theory for the kinetic Fokker-Planck equations (GIMV-2016) and the Morrey estimates (BCM-1996) to further control the velocity derivatives. This is a joint work with Y. Guo, H. J. Hwang, and Z. Ouyang.