Title and Abstract

14th, 9:00 - 10:00

Small data scattering for nonlinear Schrödinger equations without gauge invariance below the Strauss exponent

We discuss small data scattering for nonlinear Schrödinger equations with homogeneous nonlinearities that are not necessarily gauge-invariant. When the exponent of the nonlinearity is above the Strauss exponent, Kato's miniature scattering theory provides a general framework in which no special structure of the nonlinearity is essential. In the mass-subcritical range, weighted spaces provide a natural setting for scattering. However, non-gauge-invariant components produce oscillatory quadratic phases after the pseudo-conformal transform, and the standard weighted Sobolev argument used in the gauge-invariant case does not apply directly.

 In this talk, we present small data scattering in weighted spaces for a class of general homogeneous nonlinearities below the Strauss exponent. The proof uses a transformed integral equation and resolvent estimates associated with a scaled harmonic oscillator, which allow us to close the argument without imposing gauge invariance.

This talk is based on joint work with Masaki Kawamoto (Okayama) and Satoshi Masaki (Hokkaido).