Speaker: 王树茂，北京大学

Inviter: 范晨捷

Title: Blow up of the 3-D compressible Navier-Stokes equations for monatomic gas

Language: Chinese

Time & Venue: 2025.10.29 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 exponent γ= 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.