[08-30] 中国人民大学柯媛元教授学术报告

• 报告题目：Global  existence,  regularity  and  boundedness  in  a  higher-dimensional chemotaxis-Navier-Stokes  system  with  nonlinear  diffusion  and  general sensitivity

• 报告人：柯媛元  (中国人民大学)

• 报告地点：腾讯会议ID:770-301-024

• 报告时间：8月30日下午15:00-16:00

• 邀请人：高洪俊

• 报告摘要：We  consider  an  incompressible  chemotaxis-Navier-Stokes  system  with  nonlinear diffusion and rotational flux n_t+u\cdot\nabla n=\Delta n^m-\nabla\cdot(nS(x,n,c)\cdot\nabla c),x\in \Omega, t>0,c_t+u\cdot\nabla c=\Delta c-nc, x\in \Omega, t>0,u_t+\kappa(u \cdot \nabla)u+\nabla P=\Delta u+n\nabla \phi , x\in \Omega,   t>0,\nabla\cdot   u=0,x\in \Omega,   t>0in   a   bounded   domain \Omega\subset\mathbb  R^N(N=2,3)  with  smooth  boundary \partial\Omega,  where \kappa\in\mathbb R. The chemotaxtic sensitivity S is a given tensor-valued function fulfilling   |S(x,n,c)| \leq   S_0(c)   for   all   (x,n,c)\in \bar{\Omega} \times   [0, \infty)\times[0, \infty) with S_0(c) nondecreasing on [0,\infty). By introducing some new methods (see Section 4 and Section 5), we prove that under the condition m >1 and some other proper regularity hypotheses on initial data, the corresponding initial-boundary  problem  possessesat  least  one  global  weak  solution.  The  present  work also shows that the weak solution could be bounded provided that N= 2.Since S is tensor-valued, it is easy to see that the restriction on m here is optimal

主讲人简介：柯媛元，中国人民大学数学学院教授，博士生导师，党委书记兼副院长。北京市高等学校青年教学名师、北京高校优秀本科育人团队成员、中国人民大学吴玉章课程思政名师工作室首席教师。曾获宝钢优秀教师奖、北京市教学成果一等奖1项，入选北京高校青年英才、主持北京市教改项目1项、主持省部级以上重点及面上科研项目8项。

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