The Critical Conjecture of Wave Equations with Logarithmic Nonlinearity on ${\mathbb{H}}^2$

Abstract

In this paper, we verified the critical conjecture in our previous work \cite{wang2023wave} on two-dimensional hyperbolic space, that is, concerning nonlinear wave equations with logarithmic nonlinearity, which behaves like ${\left(\ln 1/|u|\right)}^{1-p}|u|$ near $u=0$, on hyperbolic spaces, we demonstrate that the critical power is $p_c(2)=3$, by proving global existence for $p>3$, as well as blow up for $p\in (1,3)$.

18 pages, 3 figures. All comments are welcome. arXiv admin note: substantial text overlap with arXiv:2304.01595