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

Luigi Forcella; Lysianne Hari

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arXiv · 1709.03101

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

Luigi Forcella·Lysianne Hari

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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 $1\leq d\leq 4$. The strategy consists in proving a suitable profile decomposition theorem in $\mathbb R^d\times \mathbb T$ to pursue a concentration-compactness \& rigidity method.

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Luigi Forcella, Lysianne Hari. 2017-09-10. Large data scattering for the defocusing NLKG on waveguide $\mathbb R^d\times\mathbb T$. https://arxiv.org/abs/1709.03101

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