Interpolation scattering for wave equations with singular potentials and singular data

2024/09/12 by Ngoc, Tran Thi, Xuan, Pham Truong
#Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Functional Analysis (math.FA) #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.2409.07867

Abstract

In this paper we investigate a construction of scattering for wave-type equations with singular potentials on the whole space ℝⁿ in a framework of weak-L^p spaces. First, we use an Yamazaki-type estimate for wave groups on Lorentz spaces and fixed point arguments to prove the global well-posedness for wave-type equations on weak-L^p spaces. Then, we provide a corresponding scattering results in such singular framework. Finally, we use also the dispersive estimates to establish the polynomial stability and improve the decay of scattering.

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