Singular vortex dynamics and nonlinear Schrodinger equations

物理和数值实验揭示了理想流体和超流体中涡丝的一种意外的动力学行为。这种意想不到的行为表现在涡旋演变过程中出现的奇异形状，如角落。这项研究旨在促进我们对涡旋细丝演化的一些著名模型以及某些密切相关的非线性薛定谔方程中这种奇点形成过程的数学理解。

Physical and numerical experiments reveal an unexpected dynamical behaviour of vortex filaments in ideal fluids and superfluids. This unexpected behaviour manifests itself in the appearance of singular shapes, such as corners, in the evolution of the vortex. The proposed research aims to advance our mathematical understanding of the processes leading to formation of such singularities in some well-known models for the evolution of vortex filaments, and in certain intimately related nonlinear Schr\"odinger equations.