报告地点：行健楼学术活动室526
邀请人：吴奕飞教授
Abstract: We study the initial-boundary value problem for the nonlinear Schrödinger equation with a nonlinear Neumann boundary condition in the half-space. In the one-dimensional case, Batal-Ozsari , (2016) established the well-posedness of the problem in $H^1$, and more recently, Hayashi--Ogawa--Sato (2025) proved well-posedness in $L^2$.However, higher-dimensional cases have not been extensively investigated. As far as the speaker is aware, the existence of $L^2$-solutions in higher dimensions has been partially studied by Ogawa--Sato--T. (2024), while other cases remain unclear. In this talk, we consider the existence of $H^1$-solutions for the problem in the higher-dimensional half-space. Our approach is based on a new representation formula for solutions to the linear problem introduced by Audiard (2019). Using this representation, we establish boundary Strichartz estimates for the linear solution, including estimates with respect to both time and spatial derivatives.
