Wave maps in dimension 1+1 with an external forcing

2024/04/14 by Zdzisław Brzeźniak, Brzeźniak, Zdzisław, Jacek Jendrej +3
Engineering · Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Waves and Solitons #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.2404.09195

openalex publication_date 2024/04/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper aims to establish the local and global well-posedness theory in L¹, inspired by the approach of Keel and Tao [Internat. Math. Res. Notices, 1998], for the forced wave map equation in the ``external'' formalism. In this context, the target manifold is treated as a submanifold of a Euclidean space. As a corollary, we reprove Zhou's [Math. Z., 1999] uniqueness result, leading to the uniqueness of weak solutions with locally finite energy. Additionally, we achieve the scattering of such solutions through a conformal compactification argument.

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