Finite time singularities in a 1D model of the quasi-geostrophic equation

被引：75
|
作者：
Chae, D
Córdoba, A
Córdoba, D
Fontelos, MA
机构：
[1] CSIC, Inst Matemat & Fis Fundamental, Madrid 28006, Spain
[2] Sungkyunkwan Univ, Dept Math, Suwon 440746, South Korea
[3] Univ Autonoma Madrid, Dept Matemat, E-28049 Madrid, Spain
[4] Univ Rey Juan Carlos, Dept Matemat Aplicada, Madrid 28933, Spain
来源：
ADVANCES IN MATHEMATICS | 2005年 / 194卷 / 01期
关键词：
quasi-geostrophic equation; nonlocal flux; singularities; complex Burgers equation;
D O I：
10.1016/j.aim.2004.06.004
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper we study 1D equations with nonlocal flux. These models have resemblance of the 2D quasi-geostrophic equation. We show the existence of singularities in finite time and construct explicit solutions to the equations where the singularities formed are shocks. For the critical viscosity case we show formation of singularities and global existence of solutions for small initial data. (c) 2004 Elsevier Inc. All rights reserved.
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页码：203 / 223
页数：21
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