论文标题
无限prandtl数字对流中密度斑块的动力学
Dynamics of density patches in infinite Prandtl number convection
论文作者
论文摘要
这项工作检查了经过修改的2D零扩散性BousSinesQ系统中密度贴片的动力学，以使动量处于较大的prandtl数量平衡中。我们建立了该系统的全局良好性，用于紧凑和有界的初始密度，然后检查斑块溶液不断发展的边界的规律性。对于$ k \ in \ {0,1,2 \} $，我们证明了$ c^{k+μ} $的全局持久性，其中$μ\ in（0,1）$，通过估计单数积分的密度贴片边界。我们通过级别的方法对最初的圆形密度贴片进行了模拟结束。模拟斑块边界形成了曲率增长的角状结构，但我们的分析表明，曲率将在所有有限的时间界定。
This work examines the dynamics of density patches in the 2D zero-diffusivity Boussinesq system modified such that momentum is in a large Prandtl number balance. We establish the global well-posedness of this system for compactly supported and bounded initial densities, and then examine the regularity of the evolving boundary of patch solutions. For $k \in \{0,1,2\}$, we prove the global in time persistence of $C^{k+μ}$-regularity, where $μ\in (0,1)$, for the density patch boundary via estimates of singular integrals. We conclude with a simulation of an initially circular density patch via a level-set method. The simulated patch boundary forms corner-like structures with growing curvature, and yet our analysis shows the curvature will be bounded for all finite times.
