Global well-posedness and scattering for the radial, defocusing, cubic wave equation with initial data in a critical Besov space

TL;DR

This paper proves global well-posedness and scattering for the radial, defocusing cubic wave equation with initial data in a critical Besov space, extending understanding of solution behavior in scale-invariant function spaces.

Contribution

It establishes the global well-posedness and scattering results for the cubic wave equation with initial data in a specific critical Besov space, which was previously unresolved.

Findings

Global solutions exist for initial data in the specified Besov space.

Solutions scatter, behaving like free waves at infinity.

The result applies to a scale-invariant subspace of the energy space.

Abstract

In this paper we prove that the cubic wave equation is globally well - posed and scattering for radial initial data lying in $B_{1,1}^{2} \times B_{1,1}^{1}$. This space of functions is a scale invariant subspace of $\dot{H}^{1/2} \times \dot{H}^{-1/2}$.