Geodesic
On the large-distance asymptotics of steady state solutions of the Navier–Stokes equations in 3D exterior domains
Annales de l'I.H.P. Analyse non linéaire, Tome 28 (2011) no. 2, pp. 303-313.

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We identify the leading term describing the behavior at large distances of the steady state solutions of the Navier–Stokes equations in 3D exterior domains with vanishing velocity at the spatial infinity.

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     title = {On the large-distance asymptotics of steady state solutions of the {Navier{\textendash}Stokes} equations in {3D} exterior domains},
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Korolev, A.; Šverák, V. On the large-distance asymptotics of steady state solutions of the Navier–Stokes equations in 3D exterior domains. Annales de l'I.H.P. Analyse non linéaire, Tome 28 (2011) no. 2, pp. 303-313. doi : 10.1016/j.anihpc.2011.01.003. http://geodesic.mathdoc.fr/articles/10.1016/j.anihpc.2011.01.003/

[1] C.J. Amick, On Lerayʼs problem of steady Navier–Stokes flow past a body in the plane, Acta Math. 161 (1988), 71-130 | MR | Zbl

[2] K.I. Babenko, On stationary solutions of the problem of flow past a body of a viscous incompressible fluid, Mat. Sb. 91 no. 133 (1973), 3-25, Math. SSSR Sb. 20 (1973), 1-25 | MR | EuDML | Zbl

[3] M.E. Bogovskii, Solution of some vector analysis problems connected with operators div and grad, Trudy Sem. S.L. Sobolev 80 no. 1 (1980), 5-40 | MR

[4] M. Cannone, G. Karch, Smooth or singular solutions to the Navier–Stokes system?, J. Differential Equations 197 no. 2 (2004), 247-274 | MR | Zbl

[5] P. Deuring, G.P. Galdi, On the asymptotic behavior of physically reasonable solutions to the stationary Navier–Stokes system in three-dimensional exterior domains with zero velocity at infinity, J. Math. Fluid Mech. 2 no. 4 (2000), 353-364 | MR | Zbl

[6] R. Finn, On the exterior stationary problem for the Navier–Stokes equations, and associated perturbation problems, Arch. Ration. Mech. Anal. 19 (1965), 363-406 | MR | Zbl

[7] G.P. Galdi, An Introduction to the Mathematical Theory of the Navier–Stokes Equations, Volumes I and II, Springer (1994) | MR

[8] L.D. Landau, A new exact solution of the Navier–Stokes equations, Dokl. Akad. Nauk SSSR 43 (1944), 299 | MR

[9] L.D. Landau, E.M. Lifschitz, Fluid Mechanics, Butterworth–Heinemann (2000) | Zbl

[10] J. Leray, Etude de diverses équations intégrales non linéaires et de quelques problèmes que pose lʼhydrodynamique, J. Math. Pures Appl. 12 (1933), 1-82 | MR | EuDML | Zbl | mathdoc-id

[11] S.A. Nazarov, K. Pileckas, On steady Stokes and Navier–Stokes problems with zero velocity at infinity in a three-dimensional exterior domain, J. Math. Kyoto Univ. 40 no. 3 (2000), 475-492 | MR | Zbl

[12] P. Plecháč, V. Šverák, Singular and regular solutions of a nonlinear parabolic system, Nonlinearity 16 no. 6 (2003), 2083-2097 | MR | Zbl

[13] V. Šverák, On Landauʼs solutions of the Navier–Stokes equations, arXiv:math/0604550 (2006) | MR

[14] V. Šverák, T.P. Tsai, On the spatial decay of 3-D steady-state Navier–Stokes flows, Comm. Partial Differential Equations 25 no. 11–12 (2000), 2107-2117 | MR | Zbl

[15] G. Tian, Z. Xin, One-point singular solutions to the Navier–Stokes equations, Topol. Methods Nonlinear Anal. 11 no. 1 (1998), 135-145 | MR | Zbl

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