Small surface tension, infinite time, and light electrons: three results on the asymptotic analysis of PDEsdissertationsFlynn, PatrickcreatorMenon, GovindReaderPausader, BenoitAdvisorGomez Serrano, JavierReaderBrown University. Department of Applied Mathematicssponsor2023ix, 279 p.born digitalThesis (Ph. D.)--Brown University, 2023thesesThis thesis is an anthology of three works, which each deal with the rigorous justification of a limit of a nonlinear PDE from kinetic theory or fluid mechanics. In the first work, with Huy Nguyen, we derive the low surface tension limit for the Muskat problem. In the second work, with Benoit Pausader, Zhimeng Ouyang, and Klaus Widmayer, we construct modified scattering operators for the Vlasov-Poisson system. In the third work, with Yan Guo, we give a rigorous derivation of the massless electron limit for the Vlasov-Poisson-Landau system.Differential equations, PartialFluidsHarmonic analysisKinetic theory of gasesEnglishRPB20230602