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SUMMARY:Global hydrostatic approximation of hyperbolic Navier-Stokes syste
 m with small Gevrey class 2 data - Ping Zhang (Chinese Academy of Sciences
 )
DTSTART:20220215T094500Z
DTEND:20220215T104500Z
UID:TALK167357@talks.cam.ac.uk
DESCRIPTION:We investigate the hydrostatic approximation of&nbsp\; a hyper
 bolic version of&nbsp\; Navier-Stokes equations\, which is&nbsp\; obtained
  by using&nbsp\; Cattaneo type law instead of Fourier law\, evolving&nbsp\
 ; in a thin strip $\\R\\times (0\,\\varepsilon)$. The formal limit of thes
 e equations is a hyperbolic Prandtl&nbsp\; type equation. We first prove t
 he global existence&nbsp\; of&nbsp\; solutions to these equations under a 
 uniform smallness assumption on the data in Gevrey $2$ class. Then we just
 ify the limit globally-in-time from the anisotropic hyperbolic Navier-Stok
 es system to the hyperbolic Prandtl system with such Gevrey $2$ class data
 . Compared with \\cite{PZZ2} for the hydrostatic approximation of 2-D clas
 sical Navier-Stokes system with analytic data\, here the initial data belo
 ng to the Gevrey $2$ class\, which is very sophisticated even for the well
 -posedness&nbsp\; of the classical Prandtl system (see \\cite{DG19\,WWZ1})
 \, furthermore\, the estimate of the pressure term in the hyperbolic Prand
 tl system arises additional difficulties. This is a joint work with M. Pai
 cu.
LOCATION:Seminar Room 1\, Newton Institute
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