Evidence of singularities for a family of contour dynamics equations

被引：76
作者：
Córdoba, D
Fontelos, MA
Mancho, AM
Rodrigo, JL
机构：
[1] CSIC, Inst Matemat & Fis Fundamental, Madrid 28006, Spain
[2] Univ Autonoma Madrid, Dept Matemat, E-28049 Madrid, Spain
[3] Yale Univ, Dept Math, New Haven, CT 06520 USA
来源：
PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA | 2005年 / 102卷 / 17期
关键词：
alpha-patches; quasi-geostrophic equation; blow-up; Euler equations; self-similar behavior;
D O I：
10.1073/pnas.0501977102
中图分类号：
O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];
学科分类号：
07 ; 0710 ; 09 ;
摘要：
In this work, we show evidence of the existence of singularities developing in finite time for a class of contour dynamics equations depending on a parameter 0 < alpha <= 1. The limiting case alpha --> 0 corresponds to 2D Euler equations, and alpha = 1 corresponds to the surface quasi-geostrophic equation. The singularity is point-like, and it is approached in a self-similar manner.
引用
收藏
页码：5949 / 5952
页数：4
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