On the existence of smooth self‐similar blowup profiles for the wave map equation |
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Authors: | Pierre Germain |
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Institution: | Courant Institute, 251 Mercer St., Room 1414, New York, NY 10012‐1185 |
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Abstract: | Consider the equivariant wave map equation from Minkowski space to a rotationally symmetric manifold N that has an equator (e.g., the sphere). In dimension 3, this paper presents a necessary and sufficient condition on N for the existence of a smooth self‐similar blowup 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 blowup profile for the (hyperbolic) wave map problem.
This has several applications to questions of regularity and uniqueness for the wave map equation. © 2008 Wiley Periodicals, Inc. |
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