Blow up for nonlinear wave-type equations with perturbed derivatives

TL;DR

This paper refines blow-up results for nonlinear wave equations with derivative perturbations, analyzing how zero-order terms influence solution blow-up based on initial data and nonlinearity.

Contribution

It introduces new conditions on zero-order terms affecting blow-up behavior in wave equations with derivative perturbations.

Findings

Refined blow-up criteria for radial initial data.

Identified conditions linking zero-order terms and blow-up.

Extended analysis to scale-invariant wave equations.

Abstract

We investigate semilinear wave-type equations that can be recast as wave equations with derivatives perturbed by zero-order terms. This framework covers several well-studied cases, including the scale-invariant wave equation. In this setting, we refine existing blow-up results for radial initial data with suitable decay, and identify conditions on the zero-order terms that govern the interplay between derivative perturbations, initial data size, and nonlinearity exponent.