学术报告（李文娟 10.20）

We consider convergence properties for  generalized Schr\"{o}dinger operators along tangential curves with less smoothness than curves with Lipschitz condition. Firstly, it was open until now on pointwise convergence of solutions to the Schr\"{o}dinger equation along non-$C^1$ curves in higher dimensional case ($n\geq 2$), we obtain the corresponding results along  a class of tangential curves in $\mathbb{R}^2$ by the broad-narrow argument and polynomial partitioning. Secondly, we get the  convergence result in $\mathbb{R}$ along a family of tangential curves. As a consequence, we obtain the sharp upper bound for $p$ in $L^p$-Schr\"{o}dinger maximal estimates along tangential curve, when smoothness of the function and the curve are fixed. This is a joint work work with Prof. Huiju Wang.