二维带形区域上Chemotaxis-Navier-Stokes方程的整体适定性

Global Well-Posedness for the Chemotaxis-Navier-Stokes Equations on a 2-D Strip Domain

本文研究了二维带形区域上带齐次Neumann-Neumann-Dirichlet边界条件的Chemotaxis-Navier-Stokes方程解的适定性问题。当该方程在平衡态附近满足一定的初始条件和假设条件时,通过建立能量泛函和利用一些不等式的方法得到该方程解的一致先验估计;最后再结合局部存在性和连续性证明了解的整体存在性。

In this paper, the solution of the Chemotaxis-Navier-Stokes equation with homogeneous Neumann-Neumann-Dirichlet boundary conditions over a two-dimensional strip domain is studied. When the equation satisfies certain initial conditions and assumptions near the equilibrium state , the uniform prior estimates of the solution of the equation are obtained by establishing energy functional and using some inequalities. Finally, the global existence of solution is proved by the combination of local existence and continuity.