报告题目1：Non-existence results of classical solutions of the wave equation with power nonlinearities of spatial derivatives

报告人：Professor Hiroyuki Takamura, Tohoku University

报告时间：2025年6月13日（周五）8:30-9:10

报告地点：20-308

报告摘要：In this talk, I will present some blow-up results of the initial value problem for nonlinear wave equations of the form, $u_{tt}-¥Delta u=|¥nabla u|^p$, as well as “lifespan” estimates of the classical solution. Its one-dimensional case is closely related to cosmology, but mathematically it is interesting to prove the critical case in high dimensions by combinations of Rammaha’s functional and “slicing” method. All the results in this talk are based on joint works with T.Sasaki, K.Shao, S.Takamatsu, C.Wang.

报告人简介：Hiroyuki Takamura，日本东北大学（Tohoku University）数学研究所教授，博导。1995年获北海道大学（Hokkaido University）理学博士学位，导师为Rentaro Agemi教授，主要研究非线性波动方程的长时间行为。于2013年12月获得日本数学会函数方程分会第五届“Hukuhara奖”等。在Comm. Partial Differential Equations,Math. Z.,J. Differential Equations,Math. Ann.等国际重要刊物上发表SCI学术论文50余篇。

报告题目2：The lifespan of solutions to system of one dimensional wave equation with the scale-invariant damping

报告人：Professor Masakazu Kato, University of Hyogo

报告时间：2025年6月13日（周五）9:15-9:55

报告地点：20-308

报告摘要：In this talk, we study general system of wave equations with time-decaying semilinear wave equations including Nakao-type problem which means systems of massless wave and scale-invariant damped wave equations in one space dimension. Our purpose of this talk is to determine the critical curve that separates the time global existence and non-existence of solutions and the sharp lifespan estimates. We obtain the lifespan estimates which are classified by total integral of the initial speeds by weighted point-wise estimates. All the results in this talk are based on joint work with T. Sasaki and H. Takamura.

报告人简介：Masakazu Kato，兵库县立大学（University of Hyogo）理学研究科材料科教授。1995年获大阪大学（Osaka University）博士学位，导师为Hideo Kubo教授。研究领域主要包括Burgers方程、趋化性方程、非线性阻尼波动方程等。在 J. Differential Equations等国际重要刊物上发表 SCI 学术论文10余篇。

报告题目3：Blow-up of solutions for discrete semilinear wave equation with the scale-invariant dissipation

报告人：Professor Kyouhei Wakasa, Muroran Institute of Technology

报告时间：2025年6月13日（周五）10:20-11:00

报告地点：20-308

报告摘要：In this talk, we consider the blow-up problem for discretized scale-invariant nonlinear dissipative wave equations. It is known that the critical exponents for undiscretized equations (continuous equations) are given by Fujita and Strauss exponents depending on the space dimensions. Our purpose is to obtain results for the discretized equations that correspond to those shown for the continuous one.The proof is based on Matsuya (2013), who showed the blow-up problem for discrete semilinear wave equations without dissipative terms, and we found that the result is sharp in the case of one and two space dimensions compared to the continuous equations.

报告人简介：Kyouhei Wakasa，室兰工业大学副教授，2015年博士毕业于北海道大学（Hokkaido University）。于2015年4月至2016年3月期间获得日本学术振兴会青年科学家研究奖学金。在J. Differential Equations，J. Funct. Anal.，Discrete Contin. Dyn. Syst.等国际重要刊物上发表SCI学术论文30余篇。

报告题目4：Low regularity ill-posedness for elastic waves and ideal compressible MHD in 3D and 2D

报告人：尹思露，杭州师范大学

报告时间：2025年6月13日（周五）11:05-11:35

报告地点：20-308

报告摘要：We construct counterexamples to the local existence of low-regularity solutions to elastic wave equations and to the ideal compressible magnetohydrodynamics (MHD) system in three and two spatial dimensions (3D and 2D). For 3D, inspired by the recent works of Christodoulou, we generalize Lindblad’s classic results on the scalar wave equation by showing that the Cauchy problems for 3D elastic waves and for 3D MHD system are ill-posed in H3(R3) and H2(R2), respectively. Both elastic waves and MHD are physical systems with multiple wave-speeds. We further prove that the ill-posedness is caused by instantaneous shock formation, which is characterized by the vanishing of the inverse foliation density. In particular, when the magnetic field is absent in MHD, we also provide a desired low-regularity ill-posedness result for the 3D compressible Euler equations, and it is sharp with respect to the regularity of the fluid velocity. Our proofs for elastic waves and for MHD are based on a coalition of a carefully designed algebraic approach and a geometric approach. To trace the nonlinear interactions of various waves, we algebraically decompose the 3D elastic waves and the 3D ideal MHD equations into 6times6 and 7times7 non-strictly hyperbolic systems. Via detailed calculations, we reveal their hidden subtle structures. With them we give a complete description of solutions’ dynamics up to the earliest singular event, when a shock forms. If time permits, we will also present the corresponding results in 2D. This talk is based on joint works with Xinliang An and Haoyang Chen.

报告人简介：尹思露，杭州师范大学副教授。从事非线性波动方程（组）以及流体力学中的偏微分方程组的分析理论，相关论文发表在Amer. J. Math.、SIAM J. Math. Anal.、J. Differential Equations等知名期刊。主持国家自然科学基金1项、省部级科研项目3项。

报告题目5：A general version of Glassey conjecture on exterior domains

报告人：邵科润，浙江大学

报告时间：2025年6月13日（周五）11:40-12:10

报告地点：20-308

报告摘要：In this talk, we focus on the existence of global solutions to semilinear wave equations on exterior domains $\mathbb{R}^n\setminus\mathcal{K}$, $n\geq2$, with small initial data and nonlinear terms $F(\partial u)$ where $F\in C^{\kappa-1}$, $\partial^{\leq\kappa-1}F(0)=0$, and $\partial^{\kappa}F\in L_\loc^\infty$ with $\kappa\geq1$. If $n\geq2$ and $\kappa>n/2$, criteria of the existence of a global solution for general initial data are provided, except for non-empty obstacles $\mathcal{K}$ when $n=2$. For $n\geq3$ and $1\leq\kappa\leq n/2$, we verify the criteria for radial solutions provided obstacles are non-empty closed balls centered at origin. These criteria are established by local energy estimates and the weighted Sobolev embedding including trace estimates. Meanwhile, for a typical class of nonlinear terms and initial data, sharp estimates of lifespan are obtained.

报告人简介：邵科润，浙江大学数学科学学院2023级硕博连读研究生。

报告题目6：Regular shock reflection problem

报告人：向伟，香港城市大学

报告时间：2025年6月14日（周六）14:30-15:10

报告地点：20-308

报告摘要：We will talk about our recent results on the regular reflection solutions for the potential flow equation and Euler equations in a natural class of self-similar solutions.

报告人简介：向伟，香港城市大学数学系教授，博士生导师。2012年博士毕业于复旦大学，2012年至2014年在牛津大学陈贵强教授指导下开展博士后研究工作。向伟教授致力于流体力学中的非线性问题的研究，在高维守恒律和激波、接触间断，以及非线性双曲-椭圆混合型方程（组）等方面的研究中取得一系列丰硕成果，并荣获Eary Career Award（2015年，由香港特别行政区大学教育资助委员会授予）和HKMS outstanding Young Scholars Award （2020年，由香港数学会授予）。目前，已在《Advances in Mathematics》,《Annals of PDE》,《Communications in Mathematical Physics》、《Archive for Rational Mechanics and Analysis》、《Comm. Partial Differential Equations》、《SIAM Journal on Mathematical Analysis》、《Annales de l’Institut Henri Poincare C, Analyse Non Linearire》、《Calc. Var. Partial Differential Equations》、《Indiana Univ. Math. J. 》等国际著名SCI数学期刊上发表学术论文数篇。

报告题目7：Two-dimensional singular Riemann problems and their application

报告人：屈爱芳，上海师范大学

报告时间：2025年6月14日（周六）15:15-15:55

报告地点：20-308

报告摘要：In this talk, we will introduce a two-dimensional singular Riemann problem for the compressible Euler equations. We will analyze the intrinsic partial differential equations governing highly singular discontinuities with mass concentration and discuss non-self-similar wave structures for pressureless flow, with brief remarks on hypersonic applications. This is joint work with Qihui Gao, Prof. Xiaozhou Yang, and Prof. Hairong Yuan.

报告人简介：屈爱芳，上海师范大学教授，博士生导师。2005年本科毕业于武汉大学数学基地班，2010年获得复旦大学基础数学专业博士学位。研究兴趣为双曲型偏微分方程理论及其应用，目前主要关注于高超音流相关数学基本理论，流体力学多尺度结构等问题。成果发表在Archive for Rational Mechanics and Analysis、SIAM Journal on Mathematical Analysis和Journal of Differential Equations等杂志上。主持过国家自然科学基金面上项目2项、青年和天元各1项，入选了上海市东方英才计划拔尖项目。

报告题目8：Global existence and asymptotic behavior of large solutions for 3D compressible Navier-Stokes and MHD equations with variable coefficients

报告人：鹿彭，浙江理工大学

报告时间：2025年6月14日（周六）16:00-16:30

报告地点：20-308

报告摘要：In this talk, we consider the Cauchy problem of 3D compressible isentropic magneto-hydrodynamics (MHD) equations with density-dependent viscosities, and full compressible Navier-Stokes equations with temperature-dependent coefficients. When the initial density and temperature is linearly equivalent to a large constant state, we prove that strong solutions exist globally in time, and converge to the constant state as time goes to infinity. There is no restriction on the size of initial velocity, magnetic field, and temperature.

报告人简介：鹿彭，浙江理工大学讲师，2022年博士毕业于复旦大学，2022-2024年于上海交通大学进行博士后研究。主要研究方向是流体力学方程组的适定性与奇异极限问题。

邀请人：无穷维动力系统和偏微分方程研究所