On the Jordan-Moore-Gibson-Thompson wave equation in hereditary fluids with quadratic gradient nonlinearity

Abstract

We prove global solvability of the third-order in time Jordan-More-Gibson-Thompson acoustic wave equation with memory in ${\mathbb{R}}^n$, where $n\ge 3$. This wave equation models ultrasonic propagation in relaxing hereditary fluids and incorporates both local and cumulative nonlinear effects. The proof of global solvability is based on a sequence of high-order energy bounds that are uniform in time, and derived under the assumption of an exponentially decaying memory kernel and sufficiently small and regular initial data.