论文标题
部分可观测时空混沌系统的无模型预测
Bubble decomposition for the harmonic map heat flow in the equivariant case
论文作者
论文摘要
我们考虑了在模棱两可的对称性下，从球体中取值的平面的谐波映射热流。众所周知，针对初始值问题的解决方案可以表现出一系列时间的气泡 - 解决方案将集中在不同尺度的谐波映射的叠加和占其余能量的身体图。我们证明这种气泡分解是独一无二的，并且及时不断发生。证明的主要新成分是由作者最近在孤子分辨率问题上用于碰撞间隔的概念。
We consider the harmonic map heat flow for maps from the plane taking values in the sphere, under equivariant symmetry. It is known that solutions to the initial value problem can exhibit bubbling along a sequence of times -- the solution decouples into a superposition of harmonic maps concentrating at different scales and a body map that accounts for the rest of the energy. We prove that this bubble decomposition is unique and occurs continuously in time. The main new ingredient in the proof is the notion of a collision interval motivated by the authors' recent work on the soliton resolution problem for equivariant wave maps.
