Equivariant self-similar wave maps from Minkowski spacetime into 3-sphere

Details Equivariant self-similar wave maps from Minkowski spacetime into 3-sphere Equivariant self-similar wave maps from Minkowski spacetime into 3-sphere

1999-10-17

arxiv.org/abs/math-ph/9910026v2

Physics

Mathematical Physics

15 pages, extended version to appear in Comm. Math. Phys

Scientific paper

10.1007/s002200000291

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 wave map 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 of 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 excitation index. Finally, we formulate a condition under which these results can be generalized to higher dimensions.

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