中国科学院数学与系统科学研究院
数学研究所
数学科学全国重点实验室
学术报告
偏微分方程讨论班
Speaker: 王树茂 （北京大学）
Inviter: 范晨捷
Language: Chinese
Title：Blow up of the 3-D compressible Navier-Stokes equations for monatomic gas
Time&Venue：2025年10月29日 (星期三）10:00 - 11:00 & 思源楼 S803
Abstract：We prove the blow-up of the 3-D isentropic compressible Navier-Stokes equations for the adiabatic exponentγ= 5/3, which corresponds to the law of monatomic gas. This is the degenerate case in the sense of Merle-Raphael-Rodnianski-Szeftel [Ann. Math 2022a, Ann. Math 2022b]. Motivated by breakthrough works [Ann. Math 2022a, Ann. Math 2022b], we first prove the existence of a sequence of smooth, self-similar imploding solutions to the compressible Euler equations for γ = 5/3, and then we use these self-similar profiles to construct smooth, asymptotically self-similar blow-up solutions to the compressible Navier-Stokes equations. This is a joint work with Feng Shao, Dongyi Wei and Zhifei Zhang.
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