Geodesic
On the solvability of initial-boundary value problems for a~viscous compressible fluid in an infinite time interval
Algebra i analiz, Tome 27 (2015) no. 3, pp. 238-271.

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The solution is estimated of the first boundary-value problem for the Navier–Stokes equations in the case of a compressible fluid in an infinite time interval; the solvability of the problem and the exponential decay of the solution as $t\to\infty$ are proved. The proof is based on the “free work” method due to Prof. M. Padula. It is shown that the method is applicable to the analysis of free boundary problems.
Keywords: Navier–Stokes equations, viscosity, anisotropic Sobolev–Slobodetski spaces. 
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V. A. Solonnikov. On the solvability of initial-boundary value problems for a~viscous compressible fluid in an infinite time interval. Algebra i analiz, Tome 27 (2015) no. 3, pp. 238-271. http://geodesic.mathdoc.fr/item/AA_2015_27_3_a11/

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