Small data scattering for the Gross-Pitaevskii equation in the 3D energy space with angular regularity

2018/04/20 Fri 15:30 - 17:30
中西 賢次

This talk is based on joint work with Zihua Guo and Zaher Hani. We study the asymptotic stability of plane wave solutions to the defocusing cubic nonlinear Schrödinger equation for initial perturbation with small energy in three space dimensions. It is known that the very long range interaction with the plane wave generates linear and quadratic modifications in the dispersive asymptotic evolution of the disturbance compared with the free Schrödinger equation. We prove the modified scattering for small initial data in the energy space with some angular regularity, extending the previous result with Gustafson and Tsai to a larger space, as well as the recent one by Killip, Murphy and Visan. The proof is different from them, exploiting the Strichartz estimate with angular average together with a quadratic transform. The latter is also different from the previous versions, with subtle cancellation in higher order terms.