題  目：De Giorgi argument for weighted $L^2 /cap L^/infty$ solutions to the non-cutoff Boltzmann equation

内容簡介：This talk fills in a gap of establishing global weighted $L^/infty$-solutions to the Boltzmann equation without angular cutoff. In order to overcome the difficulties arising from the singular cross-section and the low regularity, a De Giorgi type argument well developed for diffusion equations is crafted in this kinetic context with the help of the averaging lemma. Applying coercivity estimates and the spectral gap of the Boltzmann linearised operator in weighted $L^2$-spaces to the level sets of solutions, the strong averaging lemma yields a suitable $L^p$ estimate for such level sets that are crucial for constructing an appropriate energy functional to apply the De Giorgi argument.

報告人：Ricardo Alonso Pontifícia Universidade Católica do Rio de Janeiro

報告人簡介：Ricardo Jose Alonso currently works at the Department of Mathematics (MAT) at the Pontifícia Universidade Católica do Rio de Janeiro (PUC-Rio). Ricardo does research in Applied Mathematics, Analysis and Mathematical physics. His current projects include the study of dissipative particle systems and the assymptotic behavior of their macroscopical quantities. He is also interested in the analysis of strongly cummulative scattering events for particles and waves.He has published over 50 papers cited about 400 times by other researchers.

時間：2021年2月6日（周六）下午15：00開始

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2021年2月4日