Global existence of radial solutions for general semilinear hyperbolic systems in 3D

TL;DR

This paper proves the global existence of radial solutions for a broad class of 3D semilinear hyperbolic systems under null conditions, using innovative bilinear estimates without relying on time decay.

Contribution

It introduces a new bilinear estimate enabling global existence results for hyperbolic systems without time decay assumptions.

Findings

Global existence of radial solutions established

Effective bilinear estimate developed for systems without time decay

Boundedness of weighted BV norm demonstrated

Abstract

We study the well-posedness of radial solutions for general nonlinear hyperbolic systems in three dimensions. We give a proof of the global existence of radial solutions for general semilinear hyperbolic systems in 3D under null condition, with small scaling invariant $\dot{W}^{2,1}(\mathbb{R}^3)$ data. We obtain a bilinear estimate that is effective to the hyperbolic systems which do not have any time decay. It allows us to achieve the boundedness of the weighted BV norm of the radial solution.