偏微分方程研讨班

中科院数学与系统科学研究院

数学研究所

偏微分方程研讨班

报告人：李用声 教授  (华南理工大学)

题  目：Pointwise convergence problem of the Korteweg-de Vries-Benjamin-Ono equation

时  间：2020.12.09（星期三）, 9:00-10:00

地  点：腾讯会议，ID：416 818 705

摘  要：In this talk we discuss the pointwise convergence problem for the KdV-BO equation. First we prove that the solution $u(x,t)$ converges  pointwisely to the initial data $f(x)$ for a.e. $x\in R$ when $f\in H^s(R)$ with $s\geq\frac{1}{4}$. Then we demonstrate that the Hausdorff dimension of the divergence set of points ofthe solution is $1-2s$ when $\frac{1}{4}\leq s\leq\frac{1}{2}$.Finally we obtain the stochastic continuity for the initial data with much less regularity, i.e. for a large class of the initial data in $L^2(\R)$, via the randomization technique.

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报告人：李俊峰 教授 (大连理工大学)

题  目：The convergence of the fractional schr？dinger operator

时  间：2020.12.09（星期三）, 10:00-11:00

地  点：腾讯会议，ID：416 818 705

摘  要：In this talk, I will present our recents works on the convergence properties of the Fractional Schr？dinger operators. Moreover, We obtained an improved estimate on the upper bound of divergent set of the Schrodinger operator for a> 1. For 0 < a< 1, we considered the non-tangent convergence and the convergence property of along a curve in one dimensional case. This talk is based on the toint works with Dan Li, Jie Xiao and Jun Wang.