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arXiv · 1910.07413

On the global wellposedness of the Klein-Gordon equation for initial data in modulation spaces

Leonid Chaichenets·Nikolaos Pattakos
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Abstract

We prove global wellposedness of the Klein-Gordon equation with power nonlinearity $|u|^{\alpha-1}u$, where $\alpha\in\left[1,\frac{d}{d-2}\right]$, in dimension $d\geq3$ with initial data in $M_{p, p'}^{1}(\mathbb{R}^d)\times M_{p,p'}(\mathbb{R}^d)$ for $p$ sufficiently close to $2$. The proof is an application of the high-low method described by Bourgain [1] where the Klein-Gordon equation is studied in one dimension with cubic nonlinearity for initial data in Sobolev spaces.

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Leonid Chaichenets, Nikolaos Pattakos. 2019-10-16. On the global wellposedness of the Klein-Gordon equation for initial data in modulation spaces. https://doi.org/10.1090/proc/15497

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