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

2021/05/24 by Belkacem Said‐Houari, Said-Houari, Belkacem · 1 citation
Engineering · Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Navier-Stokes equation solutions #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.2105.11287

openalex publication_date 2021/05/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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 \citeRacke_Said₂019 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 \citeRacke_Said₂019 and show an optimal decay rate of the solution for initial data in the Besov space B_2,∞^-3/2(ℝ³), which is larger than the Lebesgue space L¹(\R³) due to the embedding L¹(ℝ% ³)\hookrightarrow B_2,∞^-3/2(ℝ³). Hence we removed the L¹-assumption on the initial data required in \citeRacke_Said₂019 in order to prove the decay estimates of the solution.

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• Global existence for a fractionally damped nonlinear Jordan--Moore--Gibson--Thompson equation

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