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arXiv · 2409.07867

Interpolation scattering for wave equations with singular potentials and singular data

Pham Truong Xuan
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Abstract

In this paper we investigate a construction of scattering for wave-type equations with singular potentials on the whole space $\mathbb{R}^n$ 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 in weak-$L^p$ spaces.

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Pham Truong Xuan. 2024-09-12. Interpolation scattering for wave equations with singular potentials and singular data. https://doi.org/10.1080/00036811.2026.2647161

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