Local Schrödinger flow into Kähler manifolds

In this paper we show that there exists a unique local smooth solution for the Cauchy problem of the Schrödinger flow for maps from a compact Riemannian manifold into a complete Kähler manifold, or from a Euclidean space Rm into a compact Kähler manifold. As a consequence, we prove that Heisenberg s...

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Bibliographic Details
Published inScience China. Mathematics Vol. 44; no. 11; pp. 1446 - 1464
Main Authors Ding, Weiyue, Wang, Youde
Format Journal Article
LanguageEnglish
Published Heidelberg Springer Nature B.V 01.11.2001
Subjects
Cauchy problems
Euclidean geometry
Flow mapping
Riemann manifold
Sobolev space
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Summary:In this paper we show that there exists a unique local smooth solution for the Cauchy problem of the Schrödinger flow for maps from a compact Riemannian manifold into a complete Kähler manifold, or from a Euclidean space Rm into a compact Kähler manifold. As a consequence, we prove that Heisenberg spin system is locally well-posed in the appropriate Sobolev spaces.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:1006-9283
1674-7283
1862-2763
1869-1862
DOI:10.1007/BF02877074