Cusp Formation for a Nonlocal Evolution Equation

被引：4
|
作者：
Hoang, Vu [1 ]
Radosz, Maria [1 ]
机构：
[1] Rice Univ, Dept Math, MS 136,Box 1892, Houston, TX 77251 USA
来源：
ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS | 2017年 / 224卷 / 03期
基金：
美国国家科学基金会;
关键词：
MODEL;
D O I：
10.1007/s00205-017-1094-3
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Cordoba et al. (Ann Math 162(3): 1377-1389, 2005) introduced a nonlocal active scalar equation as a one-dimensional analogue of the surface-quasigeostrophic equation. It has been conjectured, based on numerical evidence, that the solution forms a cusp-like singularity in finite time. Up until now, no active scalar with nonlocal flux is known for which cusp formation has been rigorously shown. In this paper, we introduce and study a nonlocal active scalar, inspired by the CordobaCordoba- Fontelos equation, and prove that either a cusp-or needle-like singularity forms in finite time.
引用
收藏
页码：1021 / 1036
页数：16
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