报告题目：From compressible to incompressible system

报告摘要：In this talk I will present some aspects of multi-scale analysis of compressible fluids and the theory on singular limits in dynamics of viscous fluids. Such approach is way to show rigorously how to obtain incompressible models from compressible ones in certain regimes. The most well known strategy is to consider so called low Mach number regime. However I will concentrate on incompressible limit problem for a reduced model for compressible non-resistive MHD keeping Mach number large. This system can also be related to a certain class of two-fluid models. By a suitable rescaling of the magnetic pressure in terms of some parameter ε > 0, by letting ε → 0 we perform the incompressible limit while keeping the Mach number of order O(1). The study is conducted in the framework of global in time finite energy weak solutions and for ill-prepared initial data. We also consider a similar problem in presence of a strong Coriolis term. The key ingredient of the proof, based on a compensated compactness argument, is the use of the transport equation (well-known in the context of two-fluid models) underlying the dynamics. Thanks to it, and differently from previous studies about the incompressible limit, we are able to identify the asymptotic of the terms of order O(ε) and to characterise their dynamics; such an information is in fact crucial to obtain a closed system in the limit. This is recent joint result with Francesco Fanelli and Young-Sam Kwon.

报告人简介：阿内塔・弗罗布莱夫斯卡 - 卡明斯卡，波兰科学院数学研究所副研究员，波兰偏微分方程、流体力学领域青年数学学者。长期从事可压缩 / 不可压缩流体方程组、非牛顿流体、多尺度流体模型、流体边界层渐近分析等方向研究，擅长利用相对熵方法、奥尔利奇空间泛函分析工具处理流体动力学中的奇异极限、区域变分等核心数学问题。她先后在《SIAM Journal on Mathematical Analysis》《Journal of Nonlinear Science》等国际权威数学期刊发表高水平学术论文，多次与欧洲多国知名数学家开展跨国合作研究，参与多项流体力学数学建模类科研项目。

报告时间：2026年7月24日 10:30-11:30

报告地点：武之楼412教室