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

Solonnikov, V.

doi:10.1090/spmj/1402

On the solvability of initial-boundary value problems for a viscous compressible fluid in an infinite time interval
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by V. A. Solonnikov

St. Petersburg Math. J. 27 (2016), 523-546

DOI: https://doi.org/10.1090/spmj/1402

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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