Smooth self-similar blow-up profiles for the wave map equation

Details Smooth self-similar blow-up profiles for the wave map equation Smooth self-similar blow-up profiles for the wave map equation

2008-06-25

arxiv.org/abs/0806.4148v1

Mathematics

Analysis of PDEs

Scientific paper

Consider the equivariant wave map equation from Minkowski space to a rotationnally symmetric manifold which has an equator (example: the sphere). In dimension 3, this article gives a necessary and sufficient condition for the existence of a smooth self-similar blow up profile. More generally, we study the relation between 1. the minimizing properties of the equator map for the (elliptic) Dirichlet energy and 2. the existence of a smooth blow-up profile for the (hyperbolic) wave map problem. Several applications of this approach are described.

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