Discontinuity of weak solutions to the 3D NSE and MHD equations in critical and supercritical spaces
Discontinuity of weak solutions to the 3D NSE and MHD equations in critical and supercritical spaces
复制标题
临界和超临界空间中 3D NSE 和 MHD 方程弱解的不连续性
DOI：
10.1016/j.jmaa.2019.123493
复制
发表时间：
2020
影响因子：
1.3
通讯作者：
Dai, Mimi
中科院分区：
文献类型：
--
作者：
Cheskidov, Alexey;Dai, Mimi
我们证明了三维不可压缩磁流体动力学（MHD）方程组由于弱解的不连续性而在很大范围内是不适定的。具体地说，我们构造了能量有限且在一定空间中很小的初始数据，使得从这个初始数据出发的MHD系统的任何Leray-Hopf型弱解在这样的空间中在时间t= 0处是不连续的.对于Navier-Stokes方程也得到了类似的结果，它将Cheskidov和Shvkirkoy关于B stec ∞，∞− 1中不适定性的结果推广到了不一定是临界的空间。范数暴胀发生的空间区域几乎与L2相接触.
We demonstrate that the three dimensional incompressible magneto-hydrodynamics (MHD) system is ill-posed due to the discontinuity of weak solutions in a wide range of spaces. Specifically, we construct initial data which has finite energy and is small in certain spaces, such that any Leray-Hopf type of weak solution to the MHD system starting from this initial data is discontinuous at time t= 0 in such spaces. An analogous result is also obtained for the Navier-Stokes equation which extends the previous result of ill-posedness in B˙∞,∞− 1 by Cheskidov and Shvydkoy to spaces that are not necessarily critical. The region of the spaces where the norm inflation occurs almost touches L 2.
$dot{B}_{infty}^{-1,infty}$ 中不可压缩磁流体动力系统的标准膨胀
影响因子：
1.4
作者：
Mimi Dai;J. Qing;M. Schonbek
通讯作者：
M. Schonbek