Cucker-Smale方程和Navier-Stokes方程耦合问题研究

Cucker-Smale方程是动力学方程最重要的方程之一，它主要用来刻画生物群体在有限的环境信息和特定的运动规则下的分布轨迹。Navier-Stokes方程是数学中最为难解的非线性方程中的一种，它是一个用连续介质力学来描述粘性牛顿流体的方程。本项目考虑Navier-Stokes方程与Cucker-Smale方程耦合问题，这不仅可以让我们更好地了解牛顿流体和生物种群之间各自的性质，还可以让我们发现它们之间的相互影响。本研究希望，通过Cucker-Smale方程中好的机制（较高的正则性）来发现Navier-Stokes方程中某些隐藏在方程背后的性质，从而促进Navier-Stokes方程的发展。

Cucker-Smale equation is one of the most important dynamic equation, which mainly describe the distribution of biological groups under limited environment information and specific movement rules. Navier-Stokes equation is one of the most difficult equation in nonlinear equation，which is describe viscous Newtonian fluid by using continuum mechanics. The project considers the coupling of Navier-Stokes and Cucker-Smale equations, it would not only help us to understand the properties of Newtonian fluid and biological groups, but also help us to discover the interaction between them. We expect our research would detect some hidden properties of Naiver-Stokes equation by the high regularity of Cucker-Smale equation, which would promote the development of Naiver-Stokes equation.