讲座题目： Global finite-energy weak solutions for a compressible two-fluid model with non-monotone pressure laws

主 讲 人：寿凌云 副教授（南京师范大学）

讲座时间：2026年6月18日（周四）上午9:00

讲座地点：钱伟长楼201会议室

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数学与数据科学学院

2026年6月15日

讲座内容简介：

We study a compressible two-fluid model on the torus \mathbb{T}^d in dimension d\geq2. It consists of two continuity equations coupled to a single momentum equation, where the pressure has an interaction structure depending on the two densities. They can be derived, for instance, from the compressible two-fluid model with equal velocities introduced by Bresch et al. (2010), as well as from a scaling limit of the Vlasov-Fokker-Planck/compressible Navier-Stokes system studied by Mellet and Vasseur (2008). We establish the global existence of weak solutions for arbitrary initial data with finite energy, and obtain quantitative estimates on the equicontinuity of the densities. Our result can apply to general pressure laws under power-type growth conditions, namely pressures controlled by terms of the form \rho^\gamma+n^\beta, with any \gamma,\beta \geq 2d/(d+2) for d=2,3 and \gamma,\beta>d/2 for d\geq4. In particular, it allows for transitions to either single-phase regime, without imposing any relation between the adiabatic exponents or between the two densities, and covers non-monotone pressure laws. The proof is based on a suitable extension of the compactness framework of Bresch and Jabin (2018) to genuinely two-variable pressure functions. This is joint work with Prof. Hai-Liang Li.

主讲人简介：

寿凌云，南京师范大学数学科学院副教授，主要从事偏微分方程研究。近年来围绕流体力学方程、动理学方程以及双曲松弛系统 等方面开展了一些研究工作，相关研究发表在Adv. Math.、Ann. Inst. H. Poincaré C Anal. Non Linéaire、J. Math. Pures Appl.、J. Lond. Math. Soc.、SIAM J. Appl. Math.等杂志，主持国家自然基金青年项目1项，中国博士后科学基金面上项目1项。