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On the solvability of initial-boundary value problems for a viscous compressible fluid in an infinite time interval

Author: V. A. Solonnikov
Original publication: Algebra i Analiz, tom 27 (2015), nomer 3.
Journal: St. Petersburg Math. J. 27 (2016), 523-546
MSC (2010): Primary 35Q30
Published electronically: March 30, 2016
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Abstract: The solution of the first boundary-value problem for the Navier-Stokes equations is estimated in the case of a compressible fluid in an infinite time interval; the solvability of the problem is proved, together with the exponential decay of the solution as $ t\to \infty $. 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.

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Additional Information

V. A. Solonnikov
Affiliation: St. Petersburg Branch, Steklov Mathematical Institute, Russian Academy of Sciences, Fontanka 27, 191023, St. Petersburg, Russia

Keywords: Navier--Stokes equations, viscosity, anisotropic Sobolev--Slobodetski spaces
Received by editor(s): December 2, 2014
Published electronically: March 30, 2016
Additional Notes: The author is thankful to E. V. Frolova, W. M. Zajaczkowski, and V. Kalantarov for useful suggestions and discussions. The work was partially supported by the EU project FLUX 319012
Dedicated: Dedicated to Nina Nicolaevna Ural’tseva with great admiration
Article copyright: © Copyright 2016 American Mathematical Society

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