学术报告
The convergence analysis of a 2D Keller-Segel-Navier-Stokes system with fast signal diffusion-向昭银（电子科技大学）
题目：The convergence analysis of a 2D Keller-Segel-Navier-Stokes system with fast signal diffusion
报告人：向昭银 教授（电子科技大学）
时间：2020年12月3日（星期四）上午10:30-11:30
地点：线上腾讯会议（会议号：301 837 892）
Abstract : In this talk, we consider the convergence of the fully parabolic-parabolic-fluid (PP-fluid) system /begin{equation*}/left/{/begin{split}&/,/partial_t n_{/epsilon }+u_/epsilon/cdot/nabla n_/epsilon=/Delta n_/epsilon - /nabla/cdot /big(/nep S(x,/nep,/cep)/cdot/nabla c_/epsilon/big), // %& /qquad x/in/Omega,/,/, t>0,//&/epsilon/partial_t c_{/epsilon} + u_/epsilon/cdot/nabla c_/epsilon= /Delta c_/epsilon-c_/epsilon+n_/epsilon, // %& /qquad x/in/Omega,/,/, t>0,// & /, /partial_t u_{/epsilon } +(u_/ep/cdot/nabla)u_/ep + /nabla P_/epsilon = /Delta u_/epsilon+n_/epsilon/nabla/phi %& /qquad x/in/Omega,/,/, t>0, /end{split}/right. /end{equation*}to the corresponding parabolic-elliptic-fluid (PE-fluid) system as $/ep/rightarrow0$ in a bounded domain $/Om/subset/mathbb{R}^2$ with smooth boundary. Under the natural volume filling hypothesis/[/big|S(x,/nep,/cep)/big| /le /f{C_S}{ (1+/nep)^{/alpha}}/]with $/al>0$ for some positive constant $C_S$, we first show the global classical solutions $(n_/ep,c_/ep,u_/ep,P_{/ep})$ of the full PP-fluid system will converge to the solution $(n, c, u, P)$ of the corresponding PE-fluid system as $/epsilon/to 0$. As a byproduct, we obtain the global well-posedness of the PE-fluid system for general large initial data. Then we establish some new exponential time decay estimates of $(n_/ep,c_/ep,u_/ep,P_{/ep})$ uniformly in $/ep$ for suitable small initial data, which in particular ensure an improvement of convergence rate on time $t$. To further explore the convergence behavior on $/ep$ and $t$, we carry out three numerical examples of different types: the nontrivial and trivial equilibriums, and the rotating aggregation. The simulation results illustrate the possibility to achieve the optimal $O(/ep)$-convergence, and show the vanishment of the deviation between the PE-fluid system and PP-fluid system over $t$ for the equilibriums, and the drastic fluctuation of error for the rotating solution. This is a joint work with Dr Min Li and Professor Guanyu Zhou.
联系人：牛冬娟
举办单位：首都师范大学77779193永利官网
首都师范大学交叉科学研究院
