Large data low regularity scattering results for the 3D wave equation on the Euclidian space

TL;DR

This paper investigates the global behavior of solutions to the 3D nonlinear wave equation with low regularity data on Euclidean space, constructing a measure to analyze solution flow and properties.

Contribution

It introduces a non-trivial measure on distributions enabling global solution flow analysis for low regularity initial data in the 3D wave equation.

Findings

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

Construction of a measure on distributions for low regularity data

Analysis of solution properties under spherical symmetry

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.