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【系综合学术报告】2024年第22期 || Existence of Rotating Stars with Variable Entropy & The modulational approximation to the water waves


报告题目:Existence of Rotating Stars with Variable Entropy

报告人:Wu Yilun (University of Oklahoma)

时间:6月5日(周三)下午14:00-15:00   地点:理科楼B302

摘要Rotating stars can be modeled by steady solutions to the Euler-Poisson equations. An extensive literature has established the existence of rotating stars for given differentially rotating angular velocity profiles. However, all of the existing results require the angular velocity to depend on the distance to the rotation axis, but not on the distance to the equatorial plane. Incidentally, all of these solutions have constant entropy within the star. In this talk, I will present a recent result which is the first that allows a general rotation profile, without restrictions. It is also the first result that allows genuinely changing entropy within the star. The variation of entropy causes the previous methods used to construct steady solutions inapplicable. We discover a div-curl reformulation of the problem and perform analysis on the resulting elliptic-hyperbolic system. This is joint work with Juhi Jang and Walter Strauss.


报告题目The modulational approximation to the water waves

报告人苏庆堂 副研究员 中国科学院数学与系统科学研究院

时间:6月5日(周三)下午15:00-16:00        地点:理科楼B302

摘要:In this talk I will discuss the modulational approximation in particular the NLS approximation to the irrotational and incompressible water waves. In particular, I will show how to use this to study the Benjamin-Feir instability of the Stokes waves in 2d water waves.