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.