Norm inflation for generalized magneto-hydrodynamic system

被引：9
|
作者：
Cheskidov, Alexey [1 ]
Dai, Mimi [1 ]
机构：
[1] Univ Illinois, Dept Math Stat & Comp Sci, Chicago, IL 60607 USA
来源：
NONLINEARITY | 2015年 / 28卷 / 01期
基金：
美国国家科学基金会;
关键词：
norm inflation; generalized magneto-hydrodynamic system; Besov spaces; interactions of plane waves; ILL-POSEDNESS; EQUATIONS; REGULARITY;
D O I：
10.1088/0951-7715/28/1/129
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We consider the incompressible magneto-hydrodynamic system with fractional powers of the Laplacian in the three-dimensional case. We discover a wide range of spaces where the norm inflation occurs and hence small initial data results are out of reach. The norm inflation occurs not only in scaling invariant ( critical) spaces, but also in supercritical and, surprisingly, subcritical ones.
引用
收藏
页码：129 / 142
页数：14
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