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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| Published in | Science China. Mathematics Vol. 44; no. 11; pp. 1446 - 1464 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Heidelberg
Springer Nature B.V
01.11.2001
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| Abstract | 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. |
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| AbstractList | 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. |
| Author | Wang, Youde Ding, Weiyue |
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| Cites_doi | 10.1007/978-3-540-69969-9 10.1007/BF02901957 10.1142/S0129167X00000568 10.1002/(SICI)1097-0312(200005)53:5<590::AID-CPA2>3.0.CO;2-R 10.1063/1.532335 10.1007/978-1-4612-5734-9 10.1007/BF01220998 10.1112/blms/20.5.385 10.1007/s101140000060 10.1142/S0129167X95000079 10.1016/0375-9601(74)90447-2 |
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| References | P. Pang (BF02877074_CR8) 2000; 16 N. Chang (BF02877074_CR10) 2000; 53 K. Nakamura (BF02877074_CR4) 1974; 48 W. Y. Ding (BF02877074_CR1) 1998; 41 L. D. Landau (BF02877074_CR2) 1935; 8 I. Eells (BF02877074_CR15) 1988; 20 BF02877074_CR9 BF02877074_CR6 Y. D. Wang (BF02877074_CR11) 1995; 6 L. Faddeev (BF02877074_CR3) 1987 H. Wang (BF02877074_CR7) 2000; 11 T. Aubin (BF02877074_CR14) 1982 Y. Zhou (BF02877074_CR5) 1991; 34 Y. D. Wang (BF02877074_CR12) 1998; 39 P. Sulem (BF02877074_CR13) 1986; 107 |
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