论文标题
全球解决趋化性边界价值问题的解决方案
Global solutions to the free boundary value problem of a chemotaxis-Navier-Stokes system
论文作者
论文摘要
在本文中，我们研究了在有限深度的三维移动域上趋化 - 纳维尔 - 螺旋杆菌系统的全球可溶性，在下面由刚性平坦的底部界定，并由自由表面界定。在实验和数值模拟中与边界描述匹配的边界条件完成系统，我们建立了在恒定状态$（0，\ hat {C}，\ Mathbf {0}）$附近的解决方案的全局存在和唯一性，其中$ \ hat {c} $是自由表面上的牛的饱和值。据我们所知，这是在时间依赖性域上进行趋化性 - 纳维尔 - 螺旋体系统良好性的第一个分析工作。
In this paper, we investigate the global solvability of the chemotaxis-Navier-Stokes system on a three-dimensional moving domain of finite depth, bounded below by a rigid flat bottom and bounded above by the free surface. Completing the system with boundary conditions that match the boundary descriptions in the experiments and numerical simulations, we establish the global existence and uniqueness of solutions near a constant state $(0,\hat{c},\mathbf{0})$, where $\hat{c}$ is the saturation value of the oxygen on the free surface. To the best of our knowledge, this is the first analytical work for the well-posedness of chemotaxis-Navier-Stokes system on a time-dependent domain.
