Robustness of strong solutions to the compressible Navier-Stokes system

Peter Bella, Eduard Feireisl, Bum Ja Jin, and Antonín Novotný

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Submission date: 11. Apr. 2014
published in: Mathematische Annalen, 362 (2015) 1-2, p. 281-303 
DOI number (of the published article): 10.1007/s00208-014-1119-2
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Abstract:
We consider the Navier-Stokes system describing the time evolution of a compressible barotropic fluid confined to a bounded spatial domain in the 3-D physical space, supplemented with the Navier's slip boundary conditions. It is shown that the class of global in time strong solutions is robust with respect to small perturbations of the initial data. Explicit qualitative estimates are given also in terms of the shape of the underlying physical domain, with applications to problems posed on thin cylinders.