Inward/outward Energy Theory of Wave Equation in Higher Dimensions

2019/12/05 by Ruipeng Shen, Shen, Ruipeng
Earth and Planetary Sciences · Mathematics · #35L05 #35L71 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Mathematical Analysis and Transform Methods #Seismic Imaging and Inversion Techniques

paper · pdf · doi:10.48550/arxiv.1912.02428

openalex publication_date 2019/12/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider the semi-linear, defocusing wave equation ∂_t² u - Δu = -|u|^p-1 u in ℝ^d with 1+4/(d-1)≤ p < 1+4/(d-2). We generalize the inward/outward energy theory and weighted Morawetz estimates in 3D to higher dimensions. As an application we show the scattering of solutions if the energy of initial data decays at a certain rate as |x| → ∞.

Citations

• On nonlinear Schrödinger equations, II.H S -solutions and unconditional well-posedness

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