L^p-estimates for the wave equation with critical magnetic field in higher dimensions

2025/04/09 by Jialu Wang, Chengbin Xu, Wang, Jialu +3
Mathematics · #Advanced Harmonic Analysis Research #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.2504.06930

openalex publication_date 2025/04/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we study the L^p-estimates for the solution to the wave equation with a scaling-critical magnetic potential in Euclidean R^N with N≥3. Inspired by the work of \citeL, we show that the operators (I+L_A)^-γe^it√L_A is bounded in L^p(ℝ^N) for 1|1/p-1/2| and t>0, where L_A is a magnetic Schrödinger operator. In particular, we derive the L^p-bounds for the sine wave propagator sin(t√L_A)L^-\frac12_A. The key ingredient is the L^p→ L^p boundedness of the analytic operator family f_w,t(L_A).

Related

• L^p-estimates for the 2D wave equation in the scaling-critical magnetic field
• L^p-estimates for the wave equation with critical magnetic potential on conical manifolds
• Uniform resolvent estimates for magnetic operators
• L^p-L^q estimates for Electromagnetic Helmholtz equation. Singular potentials
• L^p-L^q estimates for Electromagnetic Helmholtz equation