Deckelnick, Klaus Decay estimates for the compressible Navier-Stokes equations in unbounded domains. (English) Zbl 0752.35048 Math. Z. 209, No. 1, 115-130 (1992). We consider the Navier-Stokes equations for a compressible viscous and heat-conductive fluid in the half space or an exterior domain of \(\mathbb{R}^ 3\). By means of suitable differential inequalities and a-priori estimates for elliptic problems we give explicit estimates for the rate with which the instationary solution converges to the corresponding stationary state as \(t\to\infty\). Reviewer: K.Deckelnick Cited in 67 Documents MSC: 35Q30 Navier-Stokes equations 76N10 Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics 35B40 Asymptotic behavior of solutions to PDEs Keywords:differential inequalities; a-priori estimates for elliptic problems; stationary state PDF BibTeX XML Cite \textit{K. Deckelnick}, Math. Z. 209, No. 1, 115--130 (1992; Zbl 0752.35048) Full Text: DOI EuDML References: [1] Adams, R.: Sobolev spaces. New York: Academic Press 1975 · Zbl 0314.46030 [2] Alt, H.W.: Lineare Funktionalanalysis, Berlin Heidelberg New York: Springer 1985 · Zbl 0577.46001 [3] Deckelnick, K.: Das zeitasymptotische Verhalten von Lösungen der kompressiblen Navier-Stokes Gleichungen in unbeschränkten Gebieten. Preprint No. 105, SFB 256 Bonn (1990) · Zbl 0707.35120 [4] Heywood, J.G.: The Navier-Stokes equations: on the existence, regularity and decay of solutions. Indian Univ. Math. J.29, 639–681 (1980) · Zbl 0494.35077 · doi:10.1512/iumj.1980.29.29048 [5] Heywood, J.G.: A uniqueness theorem for non-stationary Navier-Stokes flow past an obstacle. Ann. Sc. Norm. Super. Pisa, Cl. Sci., IV Ser.6, 427–445 (1979) · Zbl 0437.76032 [6] Ladyzhenskaya, O.A.: The mathematical theory of viscous incompressible flow. New York: Gordon and Breach 1969 · Zbl 0184.52603 [7] Maremonti, P.: Asymptotic stability theorems for viscous fluid motions in exterior domains. Rend. Semin. Mat. Univ. Padova71, 35–72 (1984) · Zbl 0548.76047 [8] Matsumura, A., Nishida, T.: Initial boundary value problems for the equations of motion of compressible and heat-conductive fluids. Commun. Math. Phys.89, 445–464 (1983) · Zbl 0543.76099 · doi:10.1007/BF01214738 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.