报告地点：腾讯会议：106-626-016 国产自拍 305

2025.11.7 14:00--14:50报告一：Singularity formation for compressible Euler equations with exponential time-dependent damping

报告内容：In this talk, we study the compressible Euler equations with exponentially increasing time-dependent damping $e^{\lambda t}$. We establish sufficient conditions for finite-time blow-up of classical solutions, showing that derivatives can blow up if the initial derivatives are large at some point, even as damping grows exponentially. Our results impose no restriction on solution size. Moreover, for $1<\gamma<3$, we derive time-dependent lower bounds on density for all classical solutions without extra assumptions on initial data.

报告人：隋莹，女，博士，山东工商学院应用数学专业教研主任，“2024年度先进个人”。 主要研究方向为非线性泛函分析。在Discrete Contin. Dyn. Syst., Nonlinear Anal. Real World Appl., Appl. Math. Lett. 等期刊发表SCI论文20余篇，其中Top及以上2篇。合作出版山东省普通高等教育一流教材《高等数学简明教程》（第三版）。

2025.11.7 15:00--15:50报告二：Global well-posedness and asymptotic stability for the Korteweg system in critical Besov space

报告人：张建中，博士，美国数学评论《Mathematical Reviews》特邀评论员。硕士毕业于国产自拍 ，博士毕业于南京航空航天大学。主要研究方向为偏微分方程理论及其应用。在Sci. China Math., Nonlinearity, Z. Angew. Math. Phys., Proc. Amer. Math. Soc., J. Math. Fluid Mech., Nonlinear Anal. Real World Appl. 等期刊发表SCI论文近20篇。主持山东省自然科学基金1项。

报告内容： In this report, we investigate the Cauchy problem of the Korteweg system in the $L^p$-type critical Besov space. More precisely, we establish the global well-posedness and asymptotic stability of Navier-Stokes-Korteweg Equations, Euler–Korteweg equations with damping and Euler–Fourier–Korteweg System. We found that from the perspective of pure dissipation, the keteweg type dispersion term exhibits significant differences in its impact on coupled systems with different dissipation mechanisms. That is different from the work of Kawashima, Chida and Xu [Comm. Partial Differential Equations, 2022], where their focus was on common features.

2025.11.7 16:00--16:50报告三：Asymptotic stability of viscous contact wave to a radiation hydrodynamic limit model

报告内容：This talk is concerned with the large time behavior of the solutions for 1D radiation hydrodynamic limit model without viscosity and its asymptotic stability of the viscous contact discontinuity wave under the smallness assumption of the strength of the contact wave and initial perturbations. The present pressure includes a fourth-order term about the absolute temperature from radiation effect which brings the main difficulty. Furthermore, the dssipative of the system is weaker for the lack of viscosity. All these make the problem more challenging. The prove is mainly based on the energy method, including normal and radial directions energy estimates.

报告人：李凯强，男，烟台大学数学与信息科学学院副教授，硕士生导师。硕士毕业于国产自拍 ，博士毕业于上海交通大学。主要研究方向为双曲守恒律方程（组）非线性波理论以及生物趋化模型等。在J. Differential Equations, Nonlinear Anal. Real World Appl., Appl. Math. Lett., Z. Angew. Math. Phys. 等期刊发表SCI论文20余篇。主持国家自然科学基金青年项目、山东省自然科学基金青年项目及面上项目各1项，山东省高等学校“青创团队计划”团队负责人。