论文标题
Hou-Luo场景的边界层模型
Boundary layer models of the Hou-Luo scenario
论文作者
论文摘要
Finite time blow up vs global regularity question for 3D Euler equation of fluid mechanics is a major open problem. Several years ago, Luo and Hou \cite{HouLuo14} proposed a new finite time blow up scenario based on extensive numerical simulations.该方案是Axi对称的，并具有涡度的快速生长，附近的流动点的环位于装有流体的圆柱体边界的流动点。 An important role is played by a small boundary layer where intense growth is observed. Several simplified models of the scenario have been considered, all leading to finite time blow up \cite{CKY15,CHKLVY17,HORY,KT1,HL15,KY1}.在本文中，我们提出了两个模型，这些模型是专门为获得边界上流动双曲线停滞点的进化而获得洞察力的。 One model focuses on analysis of the depletion of nonlinearity effect present in the problem. Solutions to this model are shown to be globally regular.与一维模型相比，第二个模型可以看作是试图捕获边界附近的速度场，以捕获下一个准确性的顺序。 Solutions to this model blow up in finite time.
Finite time blow up vs global regularity question for 3D Euler equation of fluid mechanics is a major open problem. Several years ago, Luo and Hou \cite{HouLuo14} proposed a new finite time blow up scenario based on extensive numerical simulations. The scenario is axi-symmetric and features fast growth of vorticity near a ring of hyperbolic points of the flow located at the boundary of a cylinder containing the fluid. An important role is played by a small boundary layer where intense growth is observed. Several simplified models of the scenario have been considered, all leading to finite time blow up \cite{CKY15,CHKLVY17,HORY,KT1,HL15,KY1}. In this paper, we propose two models that are designed specifically to gain insight in the evolution of fluid near the hyperbolic stagnation point of the flow located at the boundary. One model focuses on analysis of the depletion of nonlinearity effect present in the problem. Solutions to this model are shown to be globally regular. The second model can be seen as an attempt to capture the velocity field near the boundary to the next order of accuracy compared with the one-dimensional models such as \cite{CKY15,CHKLVY17}. Solutions to this model blow up in finite time.
