SINGULAR SOLUTIONS FOR NONLOCAL SYSTEMS OF EVOLUTION EQUATIONS WITH VORTICITY STRETCHING

被引：1

作者：

Vu Hoang ^{[1
]}

Radosz, Maria ^{[1
]}

机构：

[1] Univ Texas San Antonio, Dept Math, San Antonio, TX 78249 USA

来源：

SIAM JOURNAL ON MATHEMATICAL ANALYSIS | 2020年 / 52卷 / 02期

基金：

美国国家科学基金会;

关键词：

fluid dynamics; blowup; singularity formation; vorticity control; asymptotic solution profile; TIME BLOW-UP; MODEL;

D O I：

10.1137/19M1265570

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We investigate a system of nonlocal transport equations in one spatial dimension. The system can be regarded as a model for the three-dimensional Euler equations in the hyperbolic flow scenario. We construct blowup solutions with control over the vorticity up to the blowup time. For a wide class of initial data, we determine power-law bounds for the blowup profile with an exact exponent derived from a stationary singular solution of the system.

引用

页码：2158 / 2178

页数：21

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