Large data low regularity scattering results for the wave equation on the Euclidian space

TL;DR

This paper investigates the global behavior of solutions to the 3D nonlinear wave equation with spherical symmetry on Euclidean space, constructing a measure to analyze solution properties.

Contribution

It introduces a non-trivial measure on distributions ensuring global well-posedness of the flow for the wave equation under spherical symmetry.

Findings

Existence of a full-measure set where the flow is globally defined

Construction of a measure on distributions for the wave equation

Analysis of properties of solutions under the constructed measure

Abstract

We will consider the resolution of the 3D non linear wave equation under the assumption of spherical symmetry on the Euclidian space. For this purpose, we will build a non trivial measure on distributions such that there exists a set of full measurement onto which the flow is globally defined. We will then discuss different properties of the solutions.