Local Schrodinger flow into Kahler manifolds |
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| Institution: | 1. Institute of Mathematics, Chinese Academy of Sciences, Beijing 100080, China;Institute of Mathematics, Peking University, Beijing 100871, China
2. Institute of Mathematics, Chinese Academy of Sciences, Beijing 100080, China |
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| Abstract: | In this paper we show that there exists a unique local smooth solution for the Cauchy problem of the Schrodinger flow for maps from a compact Riemannian manifold into a complete Kahler manifold, or from a Euclidean space Rm into a compact Kahler manifold. As a consequence, we prove that Heisenberg spin system is locally well-posed in the appropriate Sobolev spaces. |
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| Keywords: | Schrodinger flow Heisenberg spin system local existence Kahler manifold |
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