Chemotaxis-Navier-Stokes方程的若干问题研究

本项目主要研究现代物理学中的一个重要模型:chemotaxis-Navier-Stokes方程。拟采用调和分析方法诸如微局部分析、Fourier频谱局部化技术、Littlewood-Paley理论、Bony仿积分解、函数空间理论等来研究如下的数学问题。(1)三维chemotaxis-Navier-Stokes方程弱解的整体存在性。(2)三维带非线性项chemotaxis-Navier-Stokes方程关于轴对称初值的弱解的整体存在性。(3)三维chemotaxis-Navier-Stokes方程无粘极限问题。

The objecct of this project is to study an important model in the mordern physics:chemotaxis-Navier-Stokes equations. The harmonic analysis like micro-local analysis, Fourier localization technique, Littlewood-Paley theory, Bony’s paraproduct decomposition， the functional spaces and so on will be applied to consider the following mathematics problem: (1)the global existence of the weak solutions for the 3D chemotaxis-Navier-Stokes equations; (2)the global existence of the weak solutions for the 3D chemotaxis-Navier-Stokes equations with axisymmetric initial data and with nonlinear term;(3)the inviscid limit of the 3D chemotaxis-Navier-Stokes equations.