On stability of incompressible flow driven by buoyancy--from Fourier analysis to energy method

Speaker: Yongzhong Sun

Venue: Room 101, Haina Building 2, Zijingang Campus

Abstract: This lecture explores the stability of viscous incompressible fluids driven by buoyancy, using the Boussinesq equations as a mathematical model. The speaker will introduce a class of stationary fluid states with a strictly increasing background temperature and investigate how the fluid behaves under small perturbations of these states. The main results establish global existence and decay of such perturbations, showing that the corresponding stationary solutions are asymptotically stable under suitable conditions. The talk will also discuss extensions to the inhomogeneous incompressible Navier–Stokes equations and several open problems. Throughout the lecture, particular attention will be given to how Fourier analysis and energy methods can be combined to study the stability of nonlinear fluid systems. This is joint work with the speaker’s former Ph.D. students Lihua Dong and Jianguo Li.