Weakly coupled system of semilinear wave equations with distinct scale-invariant terms in the linear part

TL;DR

This paper determines the critical exponent for a weakly coupled system of semilinear wave equations with scale-invariant lower order terms, analyzing blow-up and global existence using test functions and L2 estimates.

Contribution

It identifies the critical exponent for such coupled wave systems with parabolic-like terms, combining blow-up and global existence results.

Findings

Critical exponent for the system is established.

Blow-up results are obtained via test functions.

Global existence is proved using L2-L2 estimates.

Abstract

In this work we determine the critical exponent for a weakly coupled system of semilinear wave equations with distinct scale-invariant lower order terms, when these terms make both equations in some sense parabolic-like. For the blow-up result the test functions method is applied, while for the global existence (in time) results we use L2-L2 estimates with additional L1 regularity.