Norm inflation for generalized magneto-hydrodynamic system

被引：10

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

页码：129 / 142

页数：14

共 16 条

[1] Ill-posedness of the Navier-Stokes equations in a critical space in 3D [J].

Bourgain, Jean ;

Pavlovic, Natasa .

JOURNAL OF FUNCTIONAL ANALYSIS, 2008, 255 (09) :2233-2247

[2]

Cannone M, 2004, HANDBOOK OF MATHEMATICAL FLUID DYNAMICS, VOL 3, P161

[3] Global regularity for the 2D MHD equations with mixed partial dissipation and magnetic diffusion [J].

Cao, Chongsheng ;

Wu, Jiahong .

ADVANCES IN MATHEMATICS, 2011, 226 (02) :1803-1822

[4] Ill-posedness for subcritical hyperdissipative Navier-Stokes equations in the largest critical spaces [J].

Cheskidov, A. ;

Shvydkoy, R. .

JOURNAL OF MATHEMATICAL PHYSICS, 2012, 53 (11)

[5] ILL-POSEDNESS OF THE BASIC EQUATIONS OF FLUID DYNAMICS IN BESOV SPACES [J].

Cheskidov, A. ;

Shvydkoy, R. .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2010, 138 (03) :1059-1067

[6]

Cheskidov A, 2014, INDIANA U MATH J, V63, P869

[7]

Dai MM, 2011, ADV DIFFERENTIAL EQU, V16, P725

[8] Well-posedness for the Navier-Stokes equations [J].

Koch, H ;

Tataru, D .

ADVANCES IN MATHEMATICS, 2001, 157 (01) :22-35

[9]

Lemarie-Rieusset P. G., 2002, CHAPMAN HALL CRC RES, V431

[10]

Schmeisser H-J., 1987, Topics in Fourier Analysis and Function Spaces, A Wiley-Interscience Publication

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