Low regularity solutions for the wave map equation into the 2-D sphere

Piero D'Ancona; Vladimir Simeonov Gueorguiev

doi:10.1007/S00209-003-0558-3

Low regularity solutions for the wave map equation into the 2-D sphere

Piero D'Ancona, Vladimir Simeonov Gueorguiev

Research output: Contribution to journal › Article

5 Citations (Scopus)

Abstract

A class of weak wave map solutions with initial data in Sobolev space of order s < 1 is studied. A non uniqueness result is proved for the case, when the target manifold is a two dimensional sphere. Using an equivariant wave map ansatz a family of self - similar solutions is constructed. This construction enables one to show ill - posedness of the inhomogeneous Cauchy problem for wave maps.

Original language	English
Pages (from-to)	227-266
Number of pages	40
Journal	Mathematische Zeitschrift
Volume	248
Issue number	2
DOIs	https://doi.org/10.1007/S00209-003-0558-3
Publication status	Published - 2004 Oct
Externally published	Yes

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ASJC Scopus subject areas

Mathematics(all)

Cite this

D'Ancona, P., & Gueorguiev, V. S. (2004). Low regularity solutions for the wave map equation into the 2-D sphere. Mathematische Zeitschrift, 248(2), 227-266. https://doi.org/10.1007/S00209-003-0558-3

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Access to Document

10.1007/S00209-003-0558-3