Large data scattering for the defocusing NLKG on waveguide ${\mathbb{R}}^d\times \mathbb{T}$

Abstract

We consider the pure-power defocusing nonlinear Klein-Gordon equation, in the energy subcritical case, posed on the product space ${\mathbb{R}}^d\times \mathbb{T}$, where $\mathbb{T}$ is the one-dimensional flat torus. In this framework, we prove that scattering holds for any initial data belonging to the energy space $H^1\times L^2$ for $1\le d\le 4$. The strategy consists in proving a suitable profile decomposition theorem in ${\mathbb{R}}^d\times \mathbb{T}$ to pursue a concentration-compactness \& rigidity method.

submitted paper. 30 pages