Zhou, Yong Asymptotic stability for the 3D Navier-Stokes equations. (English) Zbl 1142.35548 Commun. Partial Differ. Equations 30, No. 3, 323-333 (2005). Summary: We consider the 3D Navier-Stokes equations in \(\Omega\subset \mathbb{R}^3\), not necessarily bounded. We prove the asymptotic stability for weak solutions in the class \(\nabla u \in L^{\alpha}(0, \infty;L_{\gamma}(\Omega))\) for \(2/\alpha+3/\gamma=2\) with arbitrary initial and external perturbations. Cited in 18 Documents MSC: 35Q30 Navier-Stokes equations 35B35 Stability in context of PDEs 76D05 Navier-Stokes equations for incompressible viscous fluids 76D55 Flow control and optimization for incompressible viscous fluids 93D20 Asymptotic stability in control theory Keywords:asymptotic stability; Navier-Stokes equations; Stokes operator PDFBibTeX XMLCite \textit{Y. Zhou}, Commun. Partial Differ. Equations 30, No. 3, 323--333 (2005; Zbl 1142.35548) Full Text: DOI References: [1] Beirão da Veiga H., Chin. Ann. Math. 16 pp 407– (1995) [2] DOI: 10.1007/BF00279962 · Zbl 0678.35076 · doi:10.1007/BF00279962 [3] DOI: 10.1007/BF00387899 · Zbl 0756.76018 · doi:10.1007/BF00387899 [4] DOI: 10.1002/cpa.3160350604 · Zbl 0509.35067 · doi:10.1002/cpa.3160350604 [5] Constantin P., Navier–Stokes Equations (1988) · Zbl 0687.35071 [6] Hopf E., Math. Nach. 4 pp 213– (1951) · Zbl 0042.10604 · doi:10.1002/mana.3210040121 [7] Kawanago T., Electron. J. Diff. Eqs. 15 pp 23– (1998) [8] DOI: 10.1006/jfan.2000.3625 · Zbl 0970.35106 · doi:10.1006/jfan.2000.3625 [9] DOI: 10.1007/BF02572306 · Zbl 0798.35127 · doi:10.1007/BF02572306 [10] Leray J., J. Math. Pures. Appl. 12 pp 1– (1933) [11] Lions J. L., Quelques méthodes de resolution des problémes aux limites non linéaires (1969) [12] Lions P. L., Mathematical Topics in Fluid Mechanics. Vol. 1. Incompressible Models (1996) · Zbl 0866.76002 [13] DOI: 10.1081/PDE-100107819 · Zbl 1086.35077 · doi:10.1081/PDE-100107819 [14] DOI: 10.2748/tmj/1178228767 · Zbl 0568.35077 · doi:10.2748/tmj/1178228767 [15] DOI: 10.1007/BF02102642 · Zbl 0795.35082 · doi:10.1007/BF02102642 [16] Scheffer V., Pacific J. Math. 66 pp 535– (1976) · Zbl 0325.35064 · doi:10.2140/pjm.1976.66.535 [17] DOI: 10.1007/BF00253344 · Zbl 0106.18302 · doi:10.1007/BF00253344 [18] Tanabe H., Equations of Evolution (1979) · Zbl 0417.35003 [19] Tian G., Comm. Anal. Geo. 7 pp 221– (1999) 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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.