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.
2004
.
01 Pubblicazione su rivista::01a Articolo in rivista
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]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/75110
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