论文标题
能源关键波图方程的全局，非散落的解决方案
Global, Non-scattering solutions to the energy critical wave maps equation
论文作者
论文摘要
我们考虑具有两球目标的1级能量临界波图问题。使用基于匹配的渐近扩展的方法，我们构建具有拓扑学位的无限时间放松，爆破和中间类型的解决方案。更确切地说，对于可允许的，时间与时间相关的长度尺度的符号类别，我们构建了解决方案，可以将其分解为基态谐波映射（Soliton），该谐波（Soliton）由可允许的长度尺度重新尺寸，加上辐射和较小的校正，这些更正（以适当的感觉）随着时间的临近而消失了。我们的可接受长度量表包括T的正和负能力，其指数的绝对价值足够小。此外，对于所有足够大的t，我们获得了经历型或未受限制的振荡的孤子长度尺度的溶液。
We consider the 1-equivariant energy critical wave maps problem with two-sphere target. Using a method based on matched asymptotic expansions, we construct infinite time relaxation, blow-up, and intermediate types of solutions that have topological degree one. More precisely, for a symbol class of admissible, time-dependent length scales, we construct solutions which can be decomposed as a ground state harmonic map (soliton) re-scaled by an admissible length scale, plus radiation, and small corrections which vanish (in a suitable sense) as time approaches infinity. Our class of admissible length scales includes positive and negative powers of t, with exponents sufficiently small in absolute value. In addition, we obtain solutions with soliton length scale undergoing damped or undamped oscillations in a bounded set, or undergoing unbounded oscillations, for all sufficiently large t.
