Published in
Springer (part of Springer Nature), Mathematische Zeitschrift, 2(248), p. 227-266
DOI: 10.1007/s00209-003-0558-3
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Low regularity solutions for the wave map equation into the 2-D sphere
Journal article published in 2004 by
Piero Antonio D'Ancona,
Piero d’Ancona,
Vladimir Georgiev,
Vladimir Gueorguiev
This paper is available in a repository.
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archiving forbidden
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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.