Low regularity solutions for the wave map equation into the 2-D sphere

Piero D'Ancona, Vladimir Simeonov Gueorguiev

Research output: Contribution to journal › Article

5 Citations (Scopus)

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 languageEnglish
Pages (from-to)227-266
Number of pages40
JournalMathematische Zeitschrift
Volume248
Issue number2
DOIs
Publication statusPublished - 2004 Oct
Externally publishedYes

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Regularity
Ill-posedness
Self-similar Solutions
Nonuniqueness
Equivariant
Sobolev Spaces
Cauchy Problem
Target
Class
Family

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Low regularity solutions for the wave map equation into the 2-D sphere. / D'Ancona, Piero; Gueorguiev, Vladimir Simeonov.

In: Mathematische Zeitschrift, Vol. 248, No. 2, 10.2004, p. 227-266.

Research output: Contribution to journal › Article

D'Ancona, P & Gueorguiev, VS 2004, 'Low regularity solutions for the wave map equation into the 2-D sphere', Mathematische Zeitschrift, vol. 248, no. 2, pp. 227-266. https://doi.org/10.1007/S00209-003-0558-3
D'Ancona P, Gueorguiev VS. Low regularity solutions for the wave map equation into the 2-D sphere. Mathematische Zeitschrift. 2004 Oct;248(2):227-266. https://doi.org/10.1007/S00209-003-0558-3
D'Ancona, Piero ; Gueorguiev, Vladimir Simeonov. / Low regularity solutions for the wave map equation into the 2-D sphere. In: Mathematische Zeitschrift. 2004 ; Vol. 248, No. 2. pp. 227-266.
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