中科院数学与系统科学研究院
数学研究所
学术报告
调和分析和偏微分方程研讨班
报告人： Prof. Changxing Miao （Institute of Applied Physics and Computational Mathematics, Beijing）
题 目：local smoothing estimate for the Fourier integral operators satisfying cinematic conditions
时 间：2022.05.05（星期四）17:00-18:00
地 点：数学院南楼N913
摘 要：Local smoothing conjecture which was formulated by Sogge has close relationship with other significant conjectures such as Bocher-Riesz conjecture, restriction conjecture and Kakeya conjecture, and finds its extensive applications in Harmonic analysis and PDEs . In this talk, we will present the recent improvement of local smoothing estimate of a certain class of Fourier integral operators satisfying cinematic curvature conditions. The main ingredients in our proof are wave packet decomposition, the Bourgain-Guth argument and the polynomial method, variable coefficient decoupling inequality and square function estimates. This talk is based on a series of joint works with Chuanwei Gao, Bochen Liu and Yakun Xi.
----------------------------
Professor Changxing Miao currently works at the Institute of Applied Physics and Computational Mathematics, a recipient of the National Science Fund for Distinguished Young Scholars. He is well-known by his works on harmonic analysis, geometrical measure theory and the scattering theory, the mathematical theory for flow dynamics, including the works on the compressible Navier-Stokes equations with the highly oscillating initial velocity, the regularity criterion of weak solution for the 3D viscous magnetohydrodynamics equations, the Bernstein's inequality and the 2D dissipative quasi-geostrophic equation. He leads a very active research group on a project of ' PDEs, Harmonic Analysis and its application’.
附件：