半平面内涡旋演化的大时间行为
Large time behavior for vortex evolution in the half-plane
摘要：
本文从涡旋散射的角度研究了半平面中不可压缩理想流的长时间行为。我们的主要结果是，半平面涡旋动力学的某些渐近状态自然分解成一个非线性叠加的孤子状状态。我们的方法是结合弱收敛工具的涡禁闭研究中开发的技术，以研究不可压缩的二维欧拉方程的解的自相似重标度的半平面上的compensated，非负的初始涡的渐近行为。
英文摘要：
In this article we study the long-time behavior of incompressible ideal flow in a half plane from the point of view of vortex scattering. Our main result is that certain asymptotic states for half-plane vortex dynamics decompose naturally into a nonlinear superposition of soliton-like states. Our approach is to combine techniques developed in the study of vortex confinement with weak convergence tools in order to study the asymptotic behavior of a self-similar rescaling of a solution of the incompressible 2D Euler equations on a half plane with compactly supported, nonnegative initial vorticity.
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