Singular vortex dynamics and nonlinear Schrodinger equations

奇异涡动力学和非线性薛定谔方程

• 批准号: EP/J01155X/1
• 负责人: Susana Gutierez
• 金额: $ 12.65万
• 依托单位: University of Birmingham
• 依托单位国家: 英国
• 项目类别: Research Grant
• 财政年份: 2012
• 资助国家: 英国
• 起止时间: 2012 至 无数据
• 项目状态: 已结题
• 来源: https://gtr.ukri.org/projects?ref=EP%2FJ01155X%2F1
• 关键词: Singular; vortex; dynamics; nonlinear; Schrodinger

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.

物理和数值实验揭示了理想流体和超流体中涡旋细丝的一种意想不到的动力学行为。这种意想不到的行为表现在奇异形状的出现，如角落，在漩涡的演变中。提出的研究旨在促进我们对一些著名的涡丝演化模型和某些密切相关的非线性薛定谔方程中导致这种奇点形成的过程的数学理解。

项目成果

Self-similar solutions of the one-dimensional Landau-Lifshitz-Gilbert equation

一维 Landau-Lifshitz-Gilbert 方程的自相似解

• DOI: 10.48550/arxiv.1409.2340
• 发表时间: 2014
• 作者: Gutiérrez S

On the Strichartz Estimates for the Kinetic Transport Equation

关于运动输运方程的 Strichartz 估计

• DOI: 10.1080/03605302.2013.850880
• 发表时间: 2014
• 期刊: Communications in Partial Differential Equations
• 影响因子: 1.9
• 作者: Bennett J