Wave maps in dimension $1+1$ with an external forcing

Zdzisław Brzeźniak; Jacek Jendrej; Nimit Rana

Wave maps in dimension $1+1$ with an external forcing

Zdzisław Brzeźniak, Jacek Jendrej, Nimit Rana

Mathematics

Research output: Working paper › Preprint

Abstract

This paper aims to establish the local and global well-posedness theory in $L^1$, 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.

Original language	English
Publisher	Arxiv (Cornell University)
Publication status	Published - 14 Apr 2024

Bibliographical note

47 pages

Keywords

math.AP

Access to Document

2404.09195v1

Cite this

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