Norm inflation for incompressible magneto-hydrodynamic system in $\dot{B}_{\infty}^{-1,\infty}$
Norm inflation for incompressible magneto-hydrodynamic system in $\dot{B}_{\infty}^{-1,\infty}$
复制标题
$dot{B}_{infty}^{-1,infty}$ 中不可压缩磁流体动力系统的标准膨胀
DOI：
10.57262/ade/1355703204
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发表时间：
2011
影响因子：
1.4
通讯作者：
M. Schonbek
中科院分区：
文献类型：
--
作者：
Mimi Dai;J. Qing;M. Schonbek
Author（s）：Dai，Mimi; Qing，Jie; Schonbek，Maria|摘要：我们证明了三维不可压缩磁流体力学（MHD）系统的柯西问题的解可以在$\dot{B}_{\infty}^{-1，\infty}$中发展出不同类型的范数膨胀.特别是当速度很小时，磁场可以在很短的时间内发展出规范暴胀，反之亦然。对Bourgain和Pavlovi {c}构造的Navier-Stokes方程作了简要的发展.
Author(s): Dai, Mimi; Qing, Jie; Schonbek, Maria | Abstract: We demonstrate that the solutions to the Cauchy problem for the three dimensional incompressible magneto-hydrodynamics (MHD) system can develop diferent types of norm inflations in $\dot{B}_{\infty}^{-1, \infty}$. Particularly the magnetic field can develop norm inflation in short time even when the velocity remains small and vice verse. Efforts are made to present a very expository development of the inginious construction of Bourgain and Pavlovi #x27;{c} for Navier-Stokes equation.