Global stability of some totally geodesic wave maps

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:284

Article

Abbrescia, Leonardo Enrique^1,2  Chen, Yuan¹ 

[1] Michigan State Univ, E Lansing, MI 48824 USA

[2] Vanderbilt Univ, 221 Kirkland Hall, Nashville, TN 37235 USA

关键词: Totally geodesic maps;    Wave maps;    Wave-Klein-Gordon equations;    Strongly coupled nonlinearities;    Vectorfield method;    Hyperboloidal foliations;   

DOI  :  10.1016/j.jde.2021.02.056

来源: Elsevier

【 摘 要 】

We prove that wave maps that factor as R1+d ->(phi S) R ->(phi I) M, subject to a sign condition, are globally nonlinear stable under small compactly supported perturbations when Mis a spaceform. The main innovation is our assumption on phi S, namely that it be a semi-Riemannian submersion. This implies that the background solution has infinite total energy, making this, to the best of our knowledge, the first stability result for factored wave maps with infinite energy backgrounds. We prove that the equations of motion for the perturbation decouple into a nonlinear wave-Klein-Gordon system. We prove global existence for this system and improve on the known regularity assumptions for equations of this type. (C) 2021 Elsevier Inc. All rights reserved.

【 授权许可】

Free