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arXiv · 2204.01149

Singular limit for the compressible Navier--Stokes equations with the hard sphere pressure law on expanding domains

Martin Kalousek·Sarka Necasova
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Abstract

The article is devoted to 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.

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Martin Kalousek, Sarka Necasova. 2022-04-03. Singular limit for the compressible Navier--Stokes equations with the hard sphere pressure law on expanding domains. https://doi.org/10.1007/s00021-022-00750-y

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