2022
DOI: 10.48550/arxiv.2204.12525
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Nonlinear stability of the totally geodesic wave maps in non-isotropic manifolds

Abstract: In this article we investigate a type of totally geodesic map which has its image being a geodesic in an anisotropic Riemannian manifold. We consider its nonlinear stability among the family of wave maps. We first establish the factorization property and then formulate the stability problem into a PDE system in a specially constructed chart of geodesic normal coordinates. With a generalization of the hyperboloidal foliation, we establish the global existence result associate to small initial data for this PDE … Show more

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“…Finally, we want to lead one to some Dirac-related or Klein-Gordon-related works [5,8,10,16,17,22,27,28,31,33,34,40], which are also relevant to our study.…”
mentioning
confidence: 99%
“…Finally, we want to lead one to some Dirac-related or Klein-Gordon-related works [5,8,10,16,17,22,27,28,31,33,34,40], which are also relevant to our study.…”
mentioning
confidence: 99%