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.
@article{AIHPC_2011__28_2_303_0,
author = {Korolev, A. and \v{S}ver\'ak, V.},
title = {On the large-distance asymptotics of steady state solutions of the {Navier{\textendash}Stokes} equations in {3D} exterior domains},
journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
pages = {303--313},
publisher = {Elsevier},
volume = {28},
number = {2},
year = {2011},
doi = {10.1016/j.anihpc.2011.01.003},
mrnumber = {2784073},
zbl = {1216.35090},
language = {en},
url = {http://archive.numdam.org/articles/10.1016/j.anihpc.2011.01.003/}
}
TY - JOUR AU - Korolev, A. AU - Šverák, V. TI - On the large-distance asymptotics of steady state solutions of the Navier–Stokes equations in 3D exterior domains JO - Annales de l'I.H.P. Analyse non linéaire PY - 2011 SP - 303 EP - 313 VL - 28 IS - 2 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/j.anihpc.2011.01.003/ DO - 10.1016/j.anihpc.2011.01.003 LA - en ID - AIHPC_2011__28_2_303_0 ER -
%0 Journal Article %A Korolev, A. %A Šverák, V. %T On the large-distance asymptotics of steady state solutions of the Navier–Stokes equations in 3D exterior domains %J Annales de l'I.H.P. Analyse non linéaire %D 2011 %P 303-313 %V 28 %N 2 %I Elsevier %U http://archive.numdam.org/articles/10.1016/j.anihpc.2011.01.003/ %R 10.1016/j.anihpc.2011.01.003 %G en %F AIHPC_2011__28_2_303_0
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://archive.numdam.org/articles/10.1016/j.anihpc.2011.01.003/
[1] , On Lerayʼs problem of steady Navier–Stokes flow past a body in the plane, Acta Math. 161 (1988), 71-130 | MR | Zbl
[2] , 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 | EuDML | MR | Zbl
[3] , 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] , , Smooth or singular solutions to the Navier–Stokes system?, J. Differential Equations 197 no. 2 (2004), 247-274 | MR | Zbl
[5] , , 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] , 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] , An Introduction to the Mathematical Theory of the Navier–Stokes Equations, Volumes I and II, Springer (1994) | MR
[8] , A new exact solution of the Navier–Stokes equations, Dokl. Akad. Nauk SSSR 43 (1944), 299 | MR
[9] , , Fluid Mechanics, Butterworth–Heinemann (2000) | Zbl
[10] , Etude de diverses équations intégrales non linéaires et de quelques problèmes que pose lʼhydrodynamique, J. Math. Pures Appl. 12 (1933), 1-82 | EuDML | Numdam | MR | Zbl
[11] , , 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] , , Singular and regular solutions of a nonlinear parabolic system, Nonlinearity 16 no. 6 (2003), 2083-2097 | MR | Zbl
[13] , On Landauʼs solutions of the Navier–Stokes equations, arXiv:math/0604550 (2006) | MR
[14] , , 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] , , One-point singular solutions to the Navier–Stokes equations, Topol. Methods Nonlinear Anal. 11 no. 1 (1998), 135-145 | MR | Zbl
Cité par Sources :
