The mean field kinetic equation for interacting particle systems with non-Lipschitz force |
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Authors: | Qitao Yin Li Chen Simone Göttlich |
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Affiliation: | 1. Tsinghua University High School, Beijing, China;2. Department of Mathematics, University of Mannheim, Mannheim, Germany |
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Abstract: | In this paper, we prove the global existence of the weak solution to the mean field kinetic equation derived from the N-particle Newtonian system. For L1∩L∞ initial data, the solvability of the mean field kinetic equation can be obtained by using uniform estimates and compactness arguments while the difficulties arising from the nonlocal nonlinear interaction are tackled appropriately using the Aubin-Lions compact embedding theorem. |
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Keywords: | mean field limit partial differential equations Vlasov-like equations |
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