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.
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页码：2158 / 2178
页数：21
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