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SUMMARY:From the compressible Navier-Stokes equations to the primitive equ
 ations - Xin Liu (Texas A&M University)
DTSTART:20220517T111500Z
DTEND:20220517T121500Z
UID:TALK173555@talks.cam.ac.uk
DESCRIPTION:The compressible Navier-Stokes equations with small Mach numbe
 r\, it is classical to approximate the dynamics using the incompressible N
 avier-Stokes/Boussinesq equations\, and rigorous mathematical justificatio
 n has been available and widely discussed\, at least in the case without a
 ny boundary. With development of the mathematical theory of the primitive 
 equations\, the small aspect ratio limit of the incompressible Navier-Stok
 es equations has been studied\, and rigorous proof has shown the rigidity 
 of the primitive equations as a hydrostatic approximation. We consider the
  interchange of the aforementioned asymptotic limits\, and establish the c
 ompressible primitive equations as the intermediate model. It is important
  to note that\, the compressible primitive equations are the starting poin
 t of moden weather prediction and climate study\, and capture both the aco
 ustic waves due to compressibility and the hydrostatic approximation due t
 o small aspect ratio between vertical and horizontal characteristic scales
 . Both well-posedness theory and asymptotic limits are investigated for is
 entropic flows.
LOCATION:Seminar Room 1\, Newton Institute
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