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非线性偏微分方程学术研讨会
日程安排
中国 开封
2022年7月19日-21日
WilliamHill中文官方网站非线性偏微分方程学术研讨会
为了交流非线性偏微分方程及相关领域的最新研究成果，为偏微分方程及其相关领域专家、学者提供探讨，交流最新研究方向和研究成果的平台，促进偏微分方程及相关领域的发展，我们拟于2022年7月19日（周二）至21日（周四）在英国威廉希尔公司组织“WilliamHill中文官方网站非线性偏微分方程学术研讨会”（本次学术研讨会为线下会议，若疫情反复，则会议时间安排另行通知）。本次学术研讨会主要围绕非线性偏微分方程相关领域展开学术交流和讨论，关注前沿研究领域的热点问题与最新进展。我们诚邀您莅临此次学术研讨会！我们非常期待您的光临！
学术会议基本信息：
主办单位：英国威廉希尔公司
资助单位：国家自然科学基金委员会
英国威廉希尔公司
会议地点：英国威廉希尔公司二楼南阶梯教室
报到时间：2022年7月19日（周二）全天
会议日程：7月20日-7月21日上午，学术报告；7月21日下午，离会
学术委员会(按姓氏字母顺序排序):
邓引斌 (华中师范大学)
曹道民 (中科院数学与系统科学研究院)
韩小森 (WilliamHill中文官方网站)
彭双阶 (华中师范大学)
严树森 (华中师范大学)
周焕松 (武汉理工大学)
组织委员会：
主席：韩小森 (WilliamHill中文官方网站)
组织委员会成员：
刘忠原 (WilliamHill中文官方网站) 叶嵎林 (WilliamHill中文官方网站)
会议联系人：
刘忠原： WilliamHill中文官方网站 电话：15737817030 Email：liuzy@henu.edu.cn
英国威廉希尔公司
2022年7月4日
会议日程表(2022.7.20-7.21)
➢7月20日（周三全天）
8: 00–8: 30 |
开幕式 |
8:30-9:50 |
主持人： 邓引斌(华中师范大学) |
8: 30–9: 10 |
报告人：郭玉劲 (华中师范大学) |
报告题目: Local Uniqueness of Attractive Bose Gases under Rotation |
9: 10–9: 50 |
报告人：戴蔚 (北京航空航天大学)
|
报告题目: Classification of nonnegative solutions to elliptic equations involving fractional or higher order Laplacians |
9: 50—10: 20 茶 歇 |
10: 20–11: 40 |
主持人： 彭双阶(华中师范大学) |
10: 20–11: 00 |
报告人：王国栋 (哈尔滨工业大学) |
报告题目: An extension of Arnold’s second stability theorem
|
11: 00–11: 40 |
报告人：詹伟城 (厦门大学) |
报告题目: On global solutions for the gSQG equation |
午 餐 |
14: 30–15: 50 |
主持人： 周焕松(武汉理工大学) |
14: 30–15: 10 |
报告人： 郭青 (中央民族大学) |
报告题目：Infinitely many positive multi-bubbling solutions to critical Lane-Emden systems |
15: 10–15: 50 |
报告人：万捷 (北京理工大学) |
报告题目：Vortex desingularization problem of incompressible Euler equations |
15:50—16: 20 茶 歇 |
16: 20–18: 00 |
自由交流、讨论 |
晚餐 |
➢7月21日（周四上午） |
8: 30–9: 50 |
主持人： 韩丕功 (中科院数学与系统科学研究院)
|
8: 30–9: 10 |
报告人：唐仲伟 (北京师范大学) |
报告题目：Compactness of solutions to higher order elliptic equations |
9: 10–9: 50 |
报告人：罗鹏 (华中师范大学) |
报告题目：The critical points of Robin function and Kirchhoff-Routh function |
9:50—10:20 茶 歇 |
10: 20–11: 40 |
主持人：郭宗明(河南师范大学) |
10: 20–11: 00 |
报告人：钟新 (西南大学) |
报告题目：Entropy-bounded solutions to the Cauchy problem of compressible heat-conducting magnetohydrodynamic equations with far field vacuum
|
11: 00–11: 40 |
报告人：叶嵎林 (WilliamHill中文官方网站) |
报告题目：Energy equality in the isentropic compressible Navier-Stokes equations allowing vacuum |
午 餐 |
报告摘要
Classification of nonnegative solutions to elliptic equations involving fractional or higher order Laplacians
戴蔚 (北京航空航天大学)
In this report, we will talk about some recent progresses in classification results, Liouville type theorems and other basic properties of nonnegative solutions to elliptic equations involving fractional or higher order Laplacians, including arbitrary order conformally invariant equations, Hardy-Lane-Emden-Henon type equations and Schrodinger-Hartree-Maxwell type equations. This talk is based on joint works with Prof. D. Cao, T. Duyckaerts, Y. Fang, Z. Liu and G. Qin.
_________________________________________________________________
Infinitely many positive multi-bubbling solutions to critical Lane-Emden systems
郭青(中央民族大学)
We talk about the following critical elliptic systems of Hamiltonian type, which are variants of the critical Lane-Emden systems and analogous in form to the prescribed curvature problem:
where
are positive radial potentials.
Under suitable conditions on the potentials and the certain range of the exponents p and q, we construct an unbounded sequence of non-radial positive vector solutions, whose energy can be made arbitrarily large. Moreover, we prove a type of non-degeneracy result by use of various Pohozaev identities, which is of great interest independently. The indefinite linear operator and strongly coupled nonlinearities make the Hamiltonian-type systems in stark contrast both to the systems of Gradient type and to the single prescribed curvature problems. This is a joint work with J. Liu and S. Peng.
Local Uniqueness of Attractive Bose Gases under Rotation
郭玉劲 (华中师范大学)
In this talk, we focus on ground states of attractive Bose gases in a rotational trap. The local uniqueness of ground states is discussed under different assumptions on the trapping potential V(x).
_______________________________________________________________
The critical points of Robin function and Kirchhoff-Routh function
罗鹏 (华中师范大学）
The properties of Robin function and Kirchhoff-Routh function play a very basic role in the study of elliptic equation, fluid mechanics, dynamic system, geometry and topology, etc. However, the property of the critical point is still unclear for large class of domains. In this talk, we give some results on thenumber of non-degeneracy of critical pints of Robin function and Kirchhoff-Routh function. These are joint work with Francesca Gladiali, Massimo Grossi, Shusen Yan.
Compactness of solutions to higher order elliptic equations
唐仲伟 (北京师范大学）
In this talk, I will present some our recent work about the compactness of high order elliptic equations. We use blow up analysis for local integral equations to prove compactness of solutions to higher order critical elliptic equations provided the potentials only have non-degenerate zeros. Secondly, corresponding to Schoen's Weyl tensor vanishing conjecture for the Yamabe equation on manifolds, we establish a Laplacian vanishing rate of the potentials at blow up points of solutions. This is a jiont work with Miaomiao Niu and Ning Zhou.
_________________________________________________________________
Vortex desingularization problem of incompressible Euler equations
万捷(北京理工大学)
In this talk, I will introduce some recent results about the vortex desingularization problem of 3D incompressible Euler equations. For 3D axisymmetric Euler equations, we consider asymptotic behavior of vortex rings. We also discuss some results of desingularization for 3D Euler equations with helical symmetry.
An extension of Arnold’s second stability theorem
王国栋 (哈尔滨工业大学)
I will discuss a recent result on the nonlinear stability of 2D incompressible Euler flows, stating that any semistable solution to some semilinear elliptic problem with increasing nonlinearity corresponds to a stable Euler flow. The proof is based on the EC functional method by Arnold, the supporting functional method by Wolansky and Ghil, and a stability criterion by Burton.
_________________________________________________________________
Energy equality in the isentropic compressible Navier-Stokes equations allowing vacuum
叶嵎林 (WilliamHill中文官方网站)
It is well-known that a Leray-Hopf weak solution in L4(0, T; L4(T3)) for the
incompressible Navier-Stokes system is persistence of energy due to Lions. In this talk, we will show that the Lions's condition for energy balance is also valid for the weak solutions of the isentropic compressible Navier-Stokes equations allowing vacuum under suitable integrability conditions on the density and its derivative. This further allows us to establish various sufficient conditions implying energy equality for the compressible flow as well as the non-homogenous incompressible Navier-Stokes equations, which is an improvement of corresponding results obtained
by Yu in [Arch. Ration. Mech. Anal., 225 (2017)]and answers a question posed by
Liang in [Proc. Roy. Soc. Edinburgh Sect. A (2020)]. This is a joint work with
Yanqing Wang and Wei Wei.
On global solutions for the gSQG equation
詹伟城 (厦门大学)
In this talk, I will introduce some results of the existence and stability of global solutions for the generalized surface quasi-geostrophic equation. This is based on a joint work with Daomin Cao, Guolin Qin and Changjun Zou.
_________________________________________________________________
Entropy-bounded solutions to the Cauchy problem of compressible heat-conducting magnetohydrodynamic equations with far field vacuum
钟新 (西南大学)
In this talk, we will investigate the Cauchy problem to compressible heat-conducting magnetohydrodynamic equations with vacuum at infinity only. We show that the uniform boundedness of the entropy and the
regularities of the velocity and temperature can be propagated provided that the initial density decays suitably slow at infinity. The main tools are based on singularly weighted energy estimates and De Giorgi type iteration techniques developed by Li and Xin (Adv. Math., 361 2020; Comm. Pure Appl. Math., 2022; https://arxiv.org/abs/2111.14057) for the full compressible Navier-Stokes system. Some new mathematical techniques and useful estimates are developed to deduce the lower and upper bounds on the entropy. This is a joint work with Jinkai Li, Mingjie Li, and Yang Liu.
WilliamHill中文官方网站英国威廉希尔公司简介
英国威廉希尔公司是WilliamHill中文官方网站设立较早的院系之一，其前身为创建于1923年的原中州大学数理系。后历经算学系、数学系、数学与信息科学学院等阶段，2014年更名为英国威廉希尔公司，2018年获“河南省教育系统先进集体”荣誉称号。
近百年来，学院严守“明德新民、止于至善”的校训，在黄际遇、陈作钧、樊映川、黄敦慈、杜孟模、刘亚星等先后在此执教的著名数学家、教育家的引领带动下，经过几代学人的接力耕耘，形成了严谨的治学精神，积累了深厚的学术底蕴，为学院持续健康发展奠定了坚实基础。目前，学院拥有数学和统计学两个一级学科博士学位授权点和博士后科研流动站，学科教学（数学）和应用统计两个专业硕士学位授权点。数学和统计学均为河南省重点一级学科。学院开设有数学与应用数学、信息与计算科学、统计学、金融数学等四个本科专业。其中，数学与应用数学专业为国家级一流本科专业建设点、河南省专业综合改革试点专业，统计学、金融数学专业为国家级一流本科专业建设点，信息与计算科学专业为河南省一流本科专业建设点、河南省特色专业。
公司现有教职工129人，其中专任教师112人，行政教辅人员17人，博士学位获得者90人。在专任教师队伍中，有教授、副教授64人，博士、硕士生导师69人；双聘院士1人，河南省特聘教授4人，河南省讲座讲授1人；WilliamHill中文官方网站特聘教授6人，WilliamHill中文官方网站讲座教授5人，WilliamHill中文官方网站外籍“拔尖人才项目”全职特聘教授2人，WilliamHill中文官方网站“青年英才”2人；河南省教育厅学术技术带头人6人，河南省优秀青年基金获得者3人，河南省高校科技创新人才5人，形成了一支师德高尚、业务精湛、结构合理、充满活力的高水平团队队伍。
公司建有河南省应用数学中心、WilliamHill中文官方网站数学研究中心、河南省人工智能理论及算法工程研究中心、数学建模实验室、金融统计实验室和数据分析技术实验室等六个教学科研平台，拥有现代数学研究所、应用数学研究所、教学方法研究室、非线性科学研究室等四个科研机构，办有全英文专业学术刊物《数学季刊》。学院注重发挥学科带头人的引领作用，积极参与国内外学术交流，不断凝练学科研究方向，持续加强学术团队建设，在代数与数论、偏微分方程与数学物理、复分析与复几何、概率论与数理统计、科学计算、数据分析与智能处理等方向形成了比较优势和特色，取得了一批优秀科研成果。据统计，2016年—2020年，学院教师发表论文400余篇，多项成果在Advances in Mathematics，Communications in Mathematical Physics，Journal of Functional Analysis，Proceedings of the Royal Society A，Annales de l'Institut Henri Poincaré Analyse non linéaire等国际著名学术刊物上发表；获批国家自然科学基金项目38项，出版学术专著7部，荣获科研奖励100项。
公司下设数学系、应用数学系、信息与计算科学系、统计系、金融数学系、数学教育系和继续教育中心七个教学单位，现有本科生1250人，研究生247人。近年来，学院不断深化公司产品改革，探索实施分类教学、分类指导，推动完善本科生导师制度，数学与应用数学专业开设“明德计划”拔尖人才实验班，培养了一大批思想品德优良、专业知识牢固、实践能力突出、富有创新精神的高素质人才。先后有450余人次在全国老员工数学竞赛、丘成桐老员工数学竞赛和全国老员工数学建模竞赛等大型专业赛事中获奖；本科生考研录取率保持在34%以上，研究生和本科生一次性就业率均在95%以上。
展望未来，学院将全面贯彻落实党的教育方针，围绕立德树人根本任务，坚持走内涵式发展道路，加快建设成为省内领先、国内知名、有特色、高水平的研究教学型学院；在大众化教育的基础上，培养具有竞争力的拔尖创新人才和各类专门人才，为学校一流学科大学建设和地方经济发展做出应有贡献。
