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 $$\textbf{R}^3$$ . 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 $$\textbf{R}^3$$ . 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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