# Postdoc Seminar

## A Keller-Segel system with singular sensitivity in 2-D, II: Passing to the limit and "global dynamics"

### 李慧聪 博士 (华师大PDE中心博士后)

#### 2016年12月13日(周二)下午 1:00-4:00 闵行校区行政楼12楼PDE中心1202报告厅

Abstract. In the second lecture, we will first prove two strong convergence results, which allow one to pass to the limit from the approximate problems, so as to obtain the desired integral inequality and equality required in the definition of global generalized solutions. We shall also see an application of the Moser-Trudinger inequality which essentially yields some relaxation properties for both solution components. Finally, we shall show that $v(\cdot,t)\to 0$ in $L^p(\Omega)$ as $t\to\infty$ for all finite $p>1$.