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arXiv · 2402.10105

Pointwise convergence of the Klein-Gordon flow

Renato Lucà·Pablo Merino
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Abstract

We consider the PDEs version of the Carleson problem in the context of the cubic nonlinear Klein-Gordon equation. This means that we aim to establish the lowest regularity class for which one has almost everywhere pointwise convergence of the solutions to the initial data, as $t \to 0$. We prove sharp results for initial data in Sobolev spaces and for their randomized counterparts.

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Renato Lucà, Pablo Merino. 2024-02-15. Pointwise convergence of the Klein-Gordon flow. https://doi.org/10.1137/24m1656566

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