Characterization of large energy solutions of the equivariant wave map problem: I
Characterization of large energy solutions of the equivariant wave map problem: I
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DOI：
10.1353/ajm.2015.0002
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发表时间：
2012-09
影响因子：
1.7
通讯作者：
R. Cote;C. Kenig;A. Lawrie;W. Schlag
中科院分区：
文献类型：
--
作者：
R. Cote;C. Kenig;A. Lawrie;W. Schlag
本文考虑从$\Bbb{R}^{1+2}\到\Bbb{S}^2 $的能量有限的$1$-等变波映射.我们建立了一类能量小于调和映射~$Q$能量三倍的一阶整体解的分类。特别地，对于每个拓扑度为1的全局能量解，我们证明了该解渐近地收敛到一个重标调和映射加上一个辐射项。连同一个配套文章（第一部分），在那里我们考虑有限时间爆破的情况下，这给出了所有1 $-等变，度~ 1 $波映射在能量区$[E（Q），3E（Q））$的特征。
We consider $1$-equivariant wave maps from $\Bbb{R}^{1+2}\to\Bbb{S}^2$ of finite energy. We establish a classification of all degree one global solutions whose energies are less than three times the energy of the harmonic map~$Q$. In particular, for each global energy solution of topological degree one, we show that the solution asymptotically decouples into a rescaled harmonic map plus a radiation term. Together with a companion article (Part I), where we consider the case of finite-time blow up, this gives a characterization of all $1$-equivariant, degree~$1$ wave maps in the energy regime $[E(Q),3E(Q))$.