L^p-estimates for the 2D wave equation in the scaling-critical magnetic field

2025/02/05 by Wang, Jialu, Zhang, Fang, Zhang, Junyong +1
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2502.03151

Abstract

In this paper, we study the L^p-estimates for the solution to the 2D-wave equation with a scaling-critical magnetic potential. Inspired by the work of \citeFZZ, we show that the operators (I+L_A)^-γe^it√L_A is bounded in L^p(ℝ²) 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 ingredients are the construction of the kernel function and the proof of the pointwise estimate for an analytic operator family f_w,t(L_A).

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