Uniqueness of harmonic map heat flows and liquid crystal flows
Uniqueness of harmonic map heat flows and liquid crystal flows
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DOI：
10.3934/dcds.2013.33.739
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发表时间：
2012-09
影响因子：
1.1
通讯作者：
Junyu Lin
中科院分区：
文献类型：
--
作者：
Junyu Lin
本文证明了谐波映射热流和液晶流的一个极限唯一性准则。我们首先建立了从$R^n$到光滑紧致黎曼流形$N$的调和映射热流在$C([0,T),BMO_T(R^n,N))\cap L^\infty_{loc}((0,T);\dot{W}^{1,\infty}(R^n))$类下的唯一性，对于$0< T ≤ +\infty.$对于向列液晶流$(v,d)$，我们证明了温和解在$C([0,T),BMO_T^{-1}(R^n))\cap L^\infty_{loc}((0,T);L^\infty(R^n))\times C([0,T),BMO_T(R^n,S^2))\cap L^\infty_{loc}((0,T);\dot{W}^{1,\infty}(R^n))$类下的唯一性 $0< T ≤ +\infty.$
In this paper, we prove a limiting uniqueness criterion to harmonic map heat flows and liquid crystal flows. We firstly establish the uniqueness of harmonic map heat flows from $R^n$ to a smooth, compact Riemannian manifold $N$ in the class $C([0,T),BMO_T(R^n,N))\cap L^\infty_{loc}((0,T);\dot{W}^{1,\infty}(R^n))$ for $0< T ≤ +\infty.$ For the nematic liquid crystal flows $(v,d)$, we show that the mild solution is unique under the class $C([0,T),BMO_T^{-1}(R^n))\cap L^\infty_{loc}((0,T);L^\infty(R^n))\times C([0,T),BMO_T(R^n,S^2))\cap L^\infty_{loc}((0,T);\dot{W}^{1,\infty}(R^n))$ for $0< T ≤ +\infty.$