學術報告

報告人：王勇（中科院應用數學所，助理研究員）

報告人簡介：王勇現為中科院應用數學所助理研究員，于2012年7月在中科院數學與系統科學學院獲得博士學位，師從國家傑出基金獲得者黃飛敏研究員。王勇博士主要從事非線性偏微分方程的研究，特别是對可壓縮流體與Boltzmann方程的整體适應性等問題有着深入系統的研究，取得了一系列重要的成果。迄今已在Arch. Rational Mech. Anal., SIAM J.Math. Anal., J. Differential Equations等期刊上發表論文十餘篇。

題目：Global well-posedness of the Boltzmann equation with large amplitude initial data

摘要：The global well-posedness of the Boltzmann equation with initial data of large amplitude has remained a long-standing open problem. In this paper, by developing a new $L^\infty_xL^1_{v}\cap L^\infty_{x,v}$  approach,   we prove the global existence and uniqueness of mild solutions to the Boltzmann equation in the whole space or torus for a class of initial data with bounded velocity-weighted $L^\infty$ norm under some  smallness condition on $L^1_xL^\infty_v$ norm as well as  defect mass, energy and entropy so that the initial data  allow  large amplitude oscillations. Both the hard and soft potentials with angular cut-off are considered, and the large time behavior of solutions in $L^\infty_{x,v}$ norm with explicit rates of convergence is also studied.

報告時間：2016年5月23日（星期一）上午10:30---11:30

報告地點：科技樓南樓702