云亭数学讲坛2025第68讲——周寿明教授

The local well-posedness and inviscid limit for some Keller-Segel equations

发布者:徐有基发布时间:2025-07-30浏览次数:10


数学与统计学院邀请,重庆师范大学周寿明教授将为学院师生作学术报告

报告题目:The local well-posedness and inviscid limit for some Keller-Segel equations

报告摘要:In this report, we consider the qualitative analysis for a general form of n-dimension Keller-Segel system with logistic sources (include the parabolic-elliptic Keller-Segel (PEKS) system and the corresponding hyperbolic-elliptic Keller-Segel (HEKS) system). By the transport(-diffusion) theory, we first establish the local existence and uniqueness of strong solutions to  (PEKS) and (HEKS)  for the initial data in $B_{p,r}^{s}(\mathbb{R}^n)$ with $s> \max\{\frac{n}{p},\frac{1}{2}\}$, $1\leq p,r \leq\infty$ (or $s=\frac{n}{p}$, $1\leq p\leq 2n, r=1$), and also obtain the continuityof the solution map with respect to the initial data in the space  $\mathcal{C}([0;T];B^{s'}_{p,r} (\mathbb{R}^n))\cap\mathcal{C}^1([0;T];B^{s'-1}_{p,r}(\mathbb{R}^n))$for every $s'<s$ when $r=+\infty$ or $s'=s$when $r<+\infty$, and then derive a continuation criterion result for (HEKS). In addition, we prove this data-to-solution map for (PEKS) is discontinuous in the metric of $B_{2,\infty}^s$. Furthermore, we show that the inviscid limit of the (PEKS) converges to the (HEKS)  in the same topologyof Besov spaces as the initial data $u_0\in B_{p,r}^s(\mathbb{R}^n)$.


报告时间:20258310:00

报告地点:致勤楼B311会议室

邀请人:张旭萍云亭教授

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报告人简介

周寿明,重庆师范大学教授,重庆英才青年拔尖人才、巴渝青年学者,研究方向为偏微分方程及其应用。部分成果发表在JDEJNS等国内外重要数学期刊上。主持国家自然科学基金、重庆市杰青、重庆市教委重大项目等,研究成果获得重庆市自然科学三等奖、教育部博士研究生学术新人奖等。


数学与统计学院

甘肃省数学与统计学基础学科研究中心

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