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 taro,et 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.
Low regularity solutions for the wave map equation into the 2-D sphere / D'Ancona, Piero Antonio; Gueorguiev, Vladimir. - In: MATHEMATISCHE ZEITSCHRIFT. - ISSN 0025-5874. - STAMPA. - 248:2(2004), pp. 227-266. [10.1007/s00209-003-0558-3]
Low regularity solutions for the wave map equation into the 2-D sphere
D'ANCONA, Piero Antonio;GUEORGUIEV, VLADIMIR
2004
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 taro,et 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.File | Dimensione | Formato | |
---|---|---|---|
Dancona_Low-regularity_2004.pdf.pdf
solo gestori archivio
Tipologia:
Documento in Post-print (versione successiva alla peer review e accettata per la pubblicazione)
Licenza:
Tutti i diritti riservati (All rights reserved)
Dimensione
309.4 kB
Formato
Adobe PDF
|
309.4 kB | Adobe PDF | Contatta l'autore |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.