Nonlinear wave equations with slowly decaying initial data

TL;DR

This paper develops new local smoothing estimates in Besov spaces for the half-wave group and applies them to establish novel well-posedness results for the cubic nonlinear wave equation in two dimensions.

Contribution

It introduces new smoothing estimates in Besov spaces and demonstrates their application to improve well-posedness results for a nonlinear wave equation.

Findings

Established local smoothing estimates in Besov spaces.

Achieved new well-posedness results for the cubic nonlinear wave equation.

Compared results with existing Sobolev space frameworks.

Abstract

New local smoothing estimates in Besov spaces adapted to the half-wave group are proved via $\ell^2$-decoupling. We apply these estimates to obtain new well-posedness results for the cubic nonlinear wave equation in two dimensions. The results are compared to new well-posedness results in $L^p$-based Sobolev spaces.