Large time behavior for the classical wave equation with different regular data and its applications

2025/01/23 by Chen, Wenhui, Ikehata, Ryo
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2501.13487

Abstract

In this paper, we mainly consider large time behavior for the classical free wave equation u_tt-Δu=0 in ℝⁿ. We derive some large time optimal estimates for the quantity of solution ‖u(t,⋅)‖_L² with initial data belonging to L² or with additional weighted L¹ integrabilities. Particularly, some thresholds are discovered for the (local or global in time) stabilization of this quantity. We also apply these results to the wave equation with scale-invariant terms, the undamped σ-evolution equation, the critical Moore-Gibson-Thompson equation, and the linearized compressible Euler system.

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