The wave equation on metric graphs global well- posedenss with scattering for nonlinear wave equation

Abstract

We consider the generalized Korteweg-de Vries equation with a new linear estimate. We provide a close of self-adjoint Laplace operators on emteric graphs that the solutions of the associated wave equation satisfy the finite propagation speed property. We study standing waves for nonlinear Schrödinger equations with gauge field. We consider the defocusing cubic nonlinear wave equation in the energy –supercritical regine, in dimension greater or equal to six with no vertical assumptions in the initial data.