کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4589544 | 1334885 | 2016 | 51 صفحه PDF | دانلود رایگان |
In this paper we study k -equivariant wave maps from the hyperbolic plane into the 2-sphere as well as the energy critical equivariant SU(2)SU(2) Yang–Mills problem on 4-dimensional hyperbolic space. The latter problem bears many similarities to a 2-equivariant wave map into a surface of revolution. As in the case of 1-equivariant wave maps considered in [9], both problems admit a family of stationary solutions indexed by a parameter that determines how far the image of the map wraps around the target manifold. Here we show that if the image of a stationary solution is contained in a geodesically convex subset of the target, then it is asymptotically stable in the energy space. However, for a stationary solution that covers a large enough portion of the target, we prove that the Schrödinger operator obtained by linearizing about such a harmonic map admits a simple positive eigenvalue in the spectral gap. As there is no a priori nonlinear obstruction to asymptotic stability, this gives evidence for the existence of metastable states (i.e., solutions with anomalously slow decay rates) in these simple geometric models.
Journal: Journal of Functional Analysis - Volume 271, Issue 11, 1 December 2016, Pages 3111–3161