Pointwise convergence of the Klein-Gordon flow

2024/02/15 by Lucà, Renato, Merino, Pablo
#35L05 #35R60 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2402.10105

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 → 0. We prove sharp results for initial data in Sobolev spaces and for their randomized counterparts.

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