论文标题
3D平面平行MHD流的边界层扩展的稳定性
Stability of the boundary layer expansion for the 3D plane parallel MHD flow
论文作者
论文摘要
在本文中，我们建立了PrandTL边界层理论的数学有效性，用于一类粘性不可压缩的磁性水力动力学（MHD）流动的非线性平面平行流，具有速度不滑动边界条件，并为磁场完美传导壁。收敛以各种Sobolev规范显示，包括物理上重要的时空统一规范$ l^\ infty（H^1）$。另外，在具有均匀磁场的情况下，还获得了相似的收敛结果。这意味着磁场的稳定作用。此外，还考虑了高阶扩展。
In this paper, we establish the mathematical validity of the Prandtl boundary layer theory for a class of nonlinear plane parallel flows of viscous incompressible magnetohydrodynamic (MHD) flow with no-slip boundary condition of velocity and perfectly conducting wall for magnetic fields. The convergence is shown under various Sobolev norms, including the physically important space-time uniform norm $L^\infty(H^1)$. In addition, the similar convergence results are also obtained under the case with uniform magnetic fields. This implies the stabilizing effects of magnetic fields. Besides, the higher-order expansion is also considered.
