English

Pointwise convergence of the Klein-Gordon flow

Analysis of PDEs 2024-02-16 v1

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 t0t \to 0. We prove sharp results for initial data in Sobolev spaces and for their randomized counterparts.

Keywords

Cite

@article{arxiv.2402.10105,
  title  = {Pointwise convergence of the Klein-Gordon flow},
  author = {Renato Lucà and Pablo Merino},
  journal= {arXiv preprint arXiv:2402.10105},
  year   = {2024}
}