报告题目：Solutions to the non-cutoff Boltzmann equation in the grazing limit
报告人：何凌冰教授（清华大学数学系）
邀请人：熊林杰
时间：11月19日15:00-16：00（北京时间）
腾讯会议：503 327 312（无密码）
摘要：It is known that in the parameter range $-2 \leq \gamma <-2s$ spectral gap does not exist for the linearized Boltzmann operator without cutoff but it does for the linearized Landau operator. This talk is devoted to the understanding of the formation of spectral gap in this range through the grazing limit. Precisely, we study the Cauchy problems of these two classical collisional kinetic equations around global Maxwellians in torus and establish the following results that are uniform in the vanishing grazing parameter $\epsilon$: (i) spectral gap type estimates for the collision operators; (ii) global existence of small-amplitude solutions for initial data with low regularity; (iii) propagation of regularity in both space and velocity variables as well as velocity moments without smallness; (iv) global-in-time asymptotics of the Boltzmann solution toward the Landau solution at the rate $O(\epsilon)$; (v) continuous transition of decay structure of the Boltzmann operator to the Landau operator. In particular, the result in part (v) captures the uniform-in-$\epsilon$ transition of intrinsic optimal time decay structures of solutions and reveals how the spectrum of the linearized non-cutoff Boltzmann equation in the mentioned parameter range changes continuously under the grazing limit.
报告人简介：何凌冰，清华大学数学系教授。主要研究方向为流体力学中的Navier-Stokes，MHD等方程组以及统计物理中的Boltzmnn方程。近五年先后在 Ann. Sci. Éc. Norm. Supér.、Archive for Rational Mechanics and Analysis、Communications in Mathematical Physics、SIAM Journal on Mathematical Analysis、Journal of Functioal Analysis、Journal of Differential Equations、J. Stat. Phys.等国际主流数学杂志发表论文20余篇。
