A better bound on blow-up rate for the superconformal semilinear wave equation

TL;DR

This paper improves the upper bound on the blow-up rate for solutions to the superconformal semilinear wave equation in higher dimensions, refining previous estimates with a logarithmic factor.

Contribution

It introduces a sharper upper bound on the blow-up rate, specifically a $| ext{log}(T-t)|^q$ improvement over earlier results.

Findings

Enhanced blow-up rate bound with logarithmic correction

Applicable to higher-dimensional superconformal wave equations

Provides a tighter estimate compared to prior work

Abstract

We consider the semilinear wave equation in higher dimensions with superconformal power nonlinearity. The purpose of this paper is to give a new upper bound on the blow-up rate in some space-time integral, showing a $|\log(T-t)|^q$ improvement in comparison with previous results obtained in \cite{HZdcds13,KSVsurc12}.