主讲人简介：

穆春来教授，重庆大学数学与统计学院院长，教育部新世纪优秀人才，重庆市学术与技术带头人，重庆市英才计划领军人才，获教育部自然科学奖二等奖，重庆市自然科学奖二等奖，国家教学成果奖二等奖，重庆市数学会副理事长，主要从事非线性偏微分方程和生物数学理论研究，已在Math. Mod. Meth. Appl. Sci.、J. Diff. Equs、J. Dyn. Diff. Equs、Ann. Mat. Pura Appl.、J. Nonlinear Sci.、Proc. Roy. Soc. Edinburgh A、数学学报等国内外数学期刊发表论文多篇，承担了国家自然科学基金、教育部新世纪优秀人才支持计划、教育部优秀年轻教师基金、重庆市科委教委重大重点基金多项。

内容摘要：

In this talk, we first show by constructing a special initial data that the solution map for the one dimensional hyperbolic Keller-Segel equations (HKSE) starting from $u_0$ is discontinuous at $t=0$ in the metric of $B_{2,\infty}^{s}(\mathbb{R})$, $s>\frac{3}{2}$. Then, we establish the Hadamard local well-posedness result for the high dimensional HKSE in the larger Besov spaces $ B_{p,1}^{1+\frac{d}{p}}(\mathbb{R}^d)$, $1\leq p <\infty$. Moreover, we investigate the inviscid limit of the Keller-Segel equations with small diffusivity $\epsilon\Delta u$ as $\epsilon\rightarrow 0$ in the same topology of Besov spaces as the initial data. Finally, we establish two kinds of blow-up criteria for strong solutions in Besov spaces by means of the Littlewood-Paley theory. This is a joint work with Shouming Zhou, Lei Zhang and Simin Zhang.

主持人：秦玉明