偏微分方程式セミナー: Critical exponent for Schroedinger equation with nonlinear Neumann boundary conditions, 林 仲夫 氏

Time：16:30-17:30

Place：理学部4号館4-501室 (hybrid)

Organizer：黒田 紘敏、浜向 直

Speaker：林 仲夫 氏 (早稲田大学)

Title：Critical exponent for Schroedinger equation with nonlinear Neumann boundary conditions

Abstract：Schroedinger equation with the nonlinear Neumann boundary condition of the order $q$ is considered in a scale invariant space. We show that if $q>2$ and the data are in the homogeneous Sobolev space of $L^2$ type of the order $-1/(q-1) + 1/2$ (which is a scale invariant space), then small data global existence of solutions holds. We also show when $q=2$ or $1<q<2$, solutions blow up in finite time. This is a joint work with C. Li, T. Ogawa and T. Sato.