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 |
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Pages (from-to) | 227-266 |
Number of pages | 40 |
Journal | Mathematische Zeitschrift |
Volume | 248 |
Issue number | 2 |
DOIs | |
Publication status | Published - 2004 Oct 1 |
Externally published | Yes |
ASJC Scopus subject areas
- Mathematics(all)