Dispersive estimates for Klein-Gordon equations via a physical space approach

2019/09/12 by Willie Wai-Yeung Wong, Wong, Willie Wai Yeung
Earth and Planetary Sciences · Mathematics · #35A23 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Mathematical Analysis and Transform Methods #Meteorological Phenomena and Simulations

paper · pdf · doi:10.48550/arxiv.1909.05956

openalex publication_date 2019/09/12 · openalex created_date 2019/09/19 · openalex updated_date 2026/07/28

Abstract

Building on the hyperboloidal foliation approach of Lefloch and Ma, we extend Klainerman's physical-space approach to dispersive estimates to recover the frequency-restricted L¹--L^∞ dispersive estimates for Klein-Gordon equations. The hyperboloidal foliation approach naturally only provide estimates within a fixed forward light-cone, and is based on an initial data norm that is not translation invariant. Both of these problems can be handled with frequency-dependent physical-space truncations. To handle the lack of scaling symmetry for the Klein-Gordon equation and complete the argument, we also need to keep track of the effectiveness of our estimates in the vanishing mass limit.

Citations

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