论文标题
与耦合Navier滑动边界条件的不可压缩MHD的小型全球近似可控性
Small-time global approximate controllability for incompressible MHD with coupled Navier slip boundary conditions
论文作者
论文摘要
我们研究了平滑界限的二维或三维域中不可压缩的磁流失动力（MHD）流的小型全球近似可控性。对控件对每个连接的边界组件的任意非空的开放部分，而线性耦合的Navier滑动条件则沿边界的不受控制部分施加。摩擦系数的一些选择会导致相互作用的速度和磁场边界层。我们通过对相应的渐近扩展进行详细分析来获得这些层的足够耗散特性。对于某些摩擦系数，或者如果获得的对照与感应方程不兼容，则会出现额外的压力样项。我们表明，对于在平面简单连接的域和Navier Slip-nith-nith-nith-th-noctriction边界条件的各种选择中定义的问题不存在这样的术语。
We study the small-time global approximate controllability for incompressible magnetohydrodynamic (MHD) flows in smoothly bounded two- or three-dimensional domains. The controls act on arbitrary nonempty open portions of each connected boundary component, while linearly coupled Navier slip-with-friction conditions are imposed along the uncontrolled parts of the boundary. Some choices for the friction coefficients give rise to interacting velocity and magnetic field boundary layers. We obtain sufficient dissipation properties of these layers by a detailed analysis of the corresponding asymptotic expansions. For certain friction coefficients, or if the obtained controls are not compatible with the induction equation, an additional pressure-like term appears. We show that such a term does not exist for problems defined in planar simply-connected domains and various choices of Navier slip-with-friction boundary conditions.
