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

Piero D'Ancona; Vladimir Georgier

doi:10.1007/S00209-003-0558-3

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

Piero D'Ancona^*, Vladimir Georgier

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

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 language	English
Pages (from-to)	227-266
Number of pages	40
Journal	Mathematische Zeitschrift
Volume	248
Issue number	2
DOIs	https://doi.org/10.1007/S00209-003-0558-3
Publication status	Published - 2004 Oct 1
Externally published	Yes

ASJC Scopus subject areas

Mathematics(all)

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10.1007/S00209-003-0558-3

Cite this

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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.",

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AU - Georgier, Vladimir

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N2 - 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.

AB - 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.

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SN - 0025-5874

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ER -

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

Abstract

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