报告题目：Regularity estimates for the non-cutoff soft potential Boltzmann equation with rough and slowly decaying data
报告人：何凌冰教授（清华大学）
邀请人：熊林杰
时间：2月9日（周四）16:00-17：00（北京时间）
地点：数学学院425
摘要：Following the work of Caffarelli-Kohn-Nirenberg, we call a point to be a regular one of the weak solution $f=f(t,x,v)$ to the non-cutoff Boltzmann equation if $f$ is essentially bounded in a neighborhood of this point. Generally it should imply that $f$ is indeed $C^\infty_{x,v}$ in a smaller neighborhood. In the present talk, we show that the above assertion is very subtle for the Boltzmann equation because of the degenerate property and the non-local property of the collision operator. We demonstrate it via three steps: (i). Construct so-called typical rough and slowly decaying data; (ii). Prove that such kind of the data will induce the finite smoothing effect in Sobolev spaces; (iii). Prove that this finite smoothing effect property will induce the following local properties: Leibniz rule does not hold for high derivatives (even in the weak sense) and the discontinuities.
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多篇。
