Large Initial Data Global Well-Posedness for a Supercritical Wave Equation

TL;DR

This paper establishes the global well-posedness of a supercritical wave equation in three spatial dimensions for large outgoing initial data by modifying the nonlinearity projection.

Contribution

It introduces a novel approach by projecting the nonlinearity onto outgoing states to prove global solutions for supercritical wave equations.

Findings

Global solutions exist for arbitrary large outgoing initial data.

The method applies to energy-supercritical semilinear wave equations.

Modification of the nonlinearity is key to the proof.

Abstract

We prove the existence of global solutions to the focusing energy-supercritical semilinear wave equation in R^{3+1} for arbitrary outgoing large initial data, after we modify the equation by projecting the nonlinearity on outgoing states.