Justification of the Primitive equations

17.06.2021 14:50 - 15:35

Xin Liu (WIAS Berlin)


Abstract: In this talk, I will present some recent results concerning the PE diagram. Starting from compressible hydrodynamics equations, by taking the asymptotic limits of low Mach number and small aspect ratio between vertical and horizontal spatial scales, one will arrive at the now-well-known primitive equations introduced to mathematical community by Lions, Temam, Wang in 1996. Our main concern is to justify such processes. In particular, the compressible primitive equations appear as the hydrostatic approximation of atmospheric dynamics, which include the dynamics of acoustic waves. Our results establish the well-posedness of the compressible primitive equations (CPE), the existence of weak solutions to the CPE, the low Mach number limits of the CPE, and the small aspect ratio limit of the full compressible Navier-Stokes equations, all in the case of isentropic flows. In addition, some pre-results concerning remaining issues in the PE diagram will be announced without details, as well as some future perspectives.


Fakultät für Mathematik, Dekan R. I. Bot
Zoom Meeting