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arXiv · 2204.12525

Nonlinear stability of the totally geodesic wave maps in non-isotropic manifolds

Senhao Duan·Yue Ma·Weidong Zhang
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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 system, which leads to the geometric stability.

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Senhao Duan, Yue Ma, Weidong Zhang. 2022-04-26. Nonlinear stability of the totally geodesic wave maps in non-isotropic manifolds. https://arxiv.org/abs/2204.12525

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