Large data pointwise decay for defocusing semilinear wave equations

TL;DR

This paper extends pointwise decay estimates for large data solutions of defocusing semilinear wave equations beyond spherical symmetry, achieving decay rates comparable to radial and small data cases, marking a novel advancement.

Contribution

It introduces a method to improve decay estimates for large data solutions without symmetry, bridging the gap between small data and general large data cases.

Findings

Decay estimates are generalized beyond spherical symmetry.

Conformal transformation yields weak decay without symmetry.

Decay rates are improved to match radial and small data results.

Abstract

We generalize the pointwise decay estimates for large data solutions of the defocusing semilinear wave equations which we obtained earlier under restriction to spherical symmetry. Without the symmetry the conformal transformation we use provides only a weak decay. This can, however, in the next step be improved to the optimal decay estimate suggested by the radial case and small data results. This is the first result of that kind.