论文标题
连续的时间孤子分辨率,用于两泡白皮的波波图
Continuous time soliton resolution for two-bubble equivariant wave maps
论文作者
论文摘要
我们考虑了在模棱两可的情况下,我们考虑从1+2维林格夫斯基空间到2个球员的能量波图方程。我们证明,如果波图沿着一系列时间将最多的重新谐波谐波图(气泡)和辐射分解为叠加,那么这种分解会持续存在。如果均衡度等于一两个,则根据科特的顺序分辨率结果,以及Jia和Kenig的顺序分辨率,我们推断出任何具有拓扑琐碎的模糊波图,其能量小于泡沫能量的四倍,而泡沫的能量是泡沫分解为(最多两种)泡沫和辐射的四倍。
We consider the energy-critical wave maps equation from 1+2 dimensional Minkowski space into the 2-sphere, in the equivariant case. We prove that if a wave map decomposes, along a sequence of times, into a superposition of at most two rescaled harmonic maps (bubbles) and radiation, then such a decomposition holds for continuous time. If the equivariance degree equals one or two, we deduce, as a consequence of sequential soliton resolution results of Côte, and Jia and Kenig, that any topologically trivial equivariant wave map with energy less than four times the energy of the bubble asymptotically decomposes into (at most two) bubbles and radiation.