Global existence for the Jordan–Moore–Gibson–Thompson equation in Besov spaces

In this paper, we consider the Cauchy problem of a model in nonlinear acoustic, named Jordan–Moore–Gibson–Thompson equation. This equation arises as an alternative to well-known Kuznetsov acoustics. We prove global existence and optimal time decay solutions Besov spaces with minimal regularity assumption on initial data, lowering required Racke Said-Houari (Commun Contemp Math. 1–39, 2019. https://doi.org/10.1142/S0219199720500698 ) for proof existence. Using time-weighted energy method help appropriate Lyapunov-type estimates, also extend rate (2019) show solution data space $$\dot{{B}}_{2,\infty }^{-3/2}(\mathbb {R}^3)$$ , which is larger than Lebesgue $$L^1(\mathbb due embedding {R} ^3)\hookrightarrow \dot{{B}}_{2,\infty . Hence, removed $$L^1$$ -assumption order estimates solution.