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

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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
Issue number2
Publication statusPublished - 2004 Oct
Externally publishedYes


ASJC Scopus subject areas

  • Mathematics(all)

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