| Abstract: |
| Primitive Equations (PE) are an important model which is widely used in the geophysical research and the mathematical analysis. We give a rigorous mathematical derivation of inviscid compressible Primitive Equations from the Euler system in a periodic channel, utilizing the relative entropy inequality. It is a joint wotk with T.Tang.
Further, we deal with the asymptotic limit of the compressible Navier-Stokes system with a pressure obeying a hard--sphere equation of state on a domain expanding to the whole physical space $R^3$. Under the assumptions that acoustic waves generated in the case of ill-prepared data do not reach the boundary of the expanding domain in the given time interval and a certain relation between the Reynolds and Mach numbers and the radius of the expanding domain we prove that the target system is the incompressible Euler system on $R^3$. We also provide an estimate of the rate of convergence expressed in terms of characteristic numbers and the radius of domains. It is a joint work with M.Kalousek. |
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