Self-similar solutions play a crucial role in the blow-up theory for the wave-map equation; they correspond to self-similar data at the time of the blow-up. However, solutions to this equation are generally considered for data in the standard finite energy spaces (in dimension d) Hd/2 × Hd/2-1. We build up in this article solutions of the covariant wave-map equation for data which are small and of infinite energy, or large and self-similar. This provides us with a general framework which includes in particular the blowing up solutions of Shatah  and Bizon . As an application, we describe more precisely the blow-up phenomenon.
|Original language||English (US)|
|Number of pages||26|
|Journal||Communications in Partial Differential Equations|
|State||Published - Sep 2008|
- Besov space
ASJC Scopus subject areas
- Applied Mathematics