On the existence of smooth self-similar blow-up profiles for the wave-map equation
نویسنده
چکیده
Consider the equivariant wave map equation from Minkowski space to a rotationnally symmetric manifold N which has an equator (example: the sphere). In dimension 3, this article presents a necessary and sufficient condition on N for the existence of a smooth self-similar blow up profile. More generally, we study the relation between the minimizing properties of the equator map for the Dirichlet energy corresponding to the (elliptic) harmonic map problem and the existence of a smooth blow-up profile for the (hyperbolic) wave map problem. This has several applications to questions of regularity and uniqueness for the wave map equation.
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تاریخ انتشار 2008