Global existence and blow-up of solutions for a system of fractional wave equations

TL;DR

This paper studies the conditions under which solutions to a coupled system of fractional wave equations either exist globally or blow up in finite time, depending on initial data and system parameters.

Contribution

It establishes a threshold dimension for solution behavior and analyzes decay estimates for global solutions in fractional wave systems.

Findings

Existence of a critical dimension N separating global existence and blow-up.

Derivation of decay estimates for global solutions.

Identification of conditions on exponents and fractional orders.

Abstract

We investigate the Cauchy problem for a 2x2-system of weakly coupled semi-linear fractional wave equations with polynomial nonlinearities posed in R+ x RN. Under appropriate conditions on the exponents and the fractional orders of the time derivatives, it is shown that there exists a threshold value of the dimension N, for which, small data-global solutions as well as finite time blowing-up solutions exist. Furthermore, we investigate the L1-decay estimates of global solutions.