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