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University of Cambridge > Talks.cam > Isaac Newton Institute Seminar Series > Global hydrostatic approximation of hyperbolic Navier-Stokes system with small Gevrey class 2 data

## Global hydrostatic approximation of hyperbolic Navier-Stokes system with small Gevrey class 2 dataAdd to your list(s) Download to your calendar using vCal - Ping Zhang (Chinese Academy of Sciences)
- Tuesday 15 February 2022, 09:45-10:45
- Seminar Room 1, Newton Institute.
If you have a question about this talk, please contact nobody. TURW02 - Rigorous analysis of incompressible fluid models and turbulence We investigate the hydrostatic approximation of a hyperbolic version of Navier-Stokes equations, which is obtained by using Cattaneo type law instead of Fourier law, evolving in a thin strip $\R\times (0,\varepsilon)$. The formal limit of these equations is a hyperbolic Prandtl type equation. We first prove the global existence of solutions to these equations under a uniform smallness assumption on the data in Gevrey $2$ class. Then we justify the limit globally-in-time from the anisotropic hyperbolic Navier-Stokes system to the hyperbolic Prandtl system with such Gevrey $2$ class data. Compared with \cite{PZZ2} for the hydrostatic approximation of 2-D classical Navier-Stokes system with analytic data, here the initial data belong to the Gevrey $2$ class, which is very sophisticated even for the well-posedness of the classical Prandtl system (see \cite{DG19,WWZ1}), furthermore, the estimate of the pressure term in the hyperbolic Prandtl system arises additional difficulties. This is a joint work with M. Paicu. This talk is part of the Isaac Newton Institute Seminar Series series. ## This talk is included in these lists:- All CMS events
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