We prove existence of a countable family of spherically symmetric self-similar wave maps from 3+1 Minkowski spacetime into the 3-sphere. These maps can be viewed as excitations of the ground state solution found previously by Shatah. The first excitation is particularly interesting in the context of the Cauchy problem since it plays the role of a critical solution sitting at the threshold for singularity formation. We analyze the linear stability of our wave maps and show that the number of unstable modes about a given map is equal to its nodal number. Finally, we formulate a condition under which these results can be generalized to higher dimensions.
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Similar content being viewed by others Explore related subjectsDiscover the latest articles and news from researchers in related subjects, suggested using machine learning. Author information Authors and AffiliationsInstitute of Physics, Jagellonian University, Kraków, Poland, , , , , , PL
Piotr Bizoń
Received: 20 October 1999 / Accepted: 12 May 2000
About this article Cite this articleBizoń, P. Equivariant Self-Similar Wave Maps from Minkowski Spacetime into 3-Sphere. Commun. Math. Phys. 215, 45–56 (2000). https://doi.org/10.1007/s002200000291
Issue Date: December 2000
DOI: https://doi.org/10.1007/s002200000291
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