A note for the global non-existence of semirelativistic equations with non-gauge invariant power type nonlinearity

TL;DR

This paper revisits the non-existence of global solutions for certain semirelativistic equations with non-gauge invariant power nonlinearities, using a direct pointwise fractional derivative estimate approach.

Contribution

It introduces a new direct method based on pointwise fractional derivative estimates to establish non-existence results for these equations.

Findings

Proves non-existence of global solutions under specific conditions.

Provides a new proof technique for semirelativistic equations.

Highlights limitations of solutions with non-gauge invariant nonlinearities.

Abstract

The non-existence of global solutions for semirelativistic equations with non-gauge invariant power type nonlinearity is revisited by a relatively direct way with a pointwise estimate of fractional derivative of some test functions.