中文摘要：

研究CoupledVortex流，证明了在紧致带边的Hermite流形上CoupledVortex流长时问解的存在性和惟一性定理，并利用该结果和穷竭方法，讨论完备Hermite流形上的情形．得到在任意完备Hermite流形上，初始度量附加一个条件下，CoupledVortex流必有长时问解．

英文摘要：

Existence and uniqueness of the long-time solution for Coupled Vortex flow over compact Hermitian mani- fold with boundary are investigated. By using this result and exhaustion method, the long-time solution to the exist- ing problem for Coupled Vortex flow over general Hermitian manifold is also discussed.