A Review of Some Results of Kac’s Program in Kinetic Theory, M.Sc. Thesis Sharif University of Technology ; Safdari, Mohammad (Supervisor)
Abstract
This thesis is devoted to the study of suitable functional frameworks for proving propagation of chaos and mean-field limit of nonlinear Vlasov-type equations for indistinguishable particles. The Kac model is a classic example and the motivation of this functional structure. On the one hand, Kac considered a spatially homogeneous gas, and on the other hand, he reduced the problem to one-dimensional collisions and dropped the conservation of momentum assumption. Therefore, he obtained a simplified version of the Boltzmann equation, which is named after him, the Kac equation. The main results which we study are quantitative estimates
on the decay of fluctuations around the deterministic... Cataloging briefA Review of Some Results of Kac’s Program in Kinetic Theory, M.Sc. Thesis Sharif University of Technology ; Safdari, Mohammad (Supervisor)
Abstract
This thesis is devoted to the study of suitable functional frameworks for proving propagation of chaos and mean-field limit of nonlinear Vlasov-type equations for indistinguishable particles. The Kac model is a classic example and the motivation of this functional structure. On the one hand, Kac considered a spatially homogeneous gas, and on the other hand, he reduced the problem to one-dimensional collisions and dropped the conservation of momentum assumption. Therefore, he obtained a simplified version of the Boltzmann equation, which is named after him, the Kac equation. The main results which we study are quantitative estimates
on the decay of fluctuations around the deterministic... Find in contentBookmark
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