Concentration-compactness and universal profiles for the non-radial energy critical wave equation

TL;DR

This paper reviews and extends the application of concentration-compactness methods to analyze global behavior, scattering, blow-up, and universal profiles for the energy critical wave equation without radial symmetry.

Contribution

It introduces new results and proofs in the non-radial setting, advancing understanding of the energy critical wave equation's solutions.

Findings

Established global well-posedness and scattering results.

Characterized blow-up solutions and universal profiles.

Extended concentration-compactness techniques to non-radial cases.

Abstract

In this paper, we give an overview of the authors' work on applications of the method of concentration-compactness to global well-posedness, scattering, blow-up and universal profiles for the energy critical wave equation in the non-radial setting. New results and proofs are also given.