报告人：Prof. Kenji Nakanishi（Kyoto University）
地点：Room 1365, Sciences Building No. 1
Abstract: The Zakharov system consists of the Schrodinger equation and the wave equation
coupled by quadratic interactions, describing the nonlinear waves in plasma. We study global
behavior of the solutions in the energy space of four space dimensions. Although the 4D setting
is not physical, it exhibits interesting energy-critical features for the analysis of dispersive PDE's.
We prove dichotomy of global behavior into scattering and weak blow-up below the ground state
energy under the radial symmetry constraint. A novel ingredient, which may be of independent
interest, is a global Strichartz estimate with uniform constant for the Schrodinger equation with
a potential solving the wave equation under the same constraints. This is joint work with Zihua Guo.