@article{AIHPC_2008__25_4_713_0,
author = {Shvydkoy, Roman and Friedlander, Susan},
title = {The unstable spectrum of the {Navier-Stokes} operator in the limit of vanishing viscosity},
journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
pages = {713--724},
year = {2008},
publisher = {Elsevier},
volume = {25},
number = {4},
doi = {10.1016/j.anihpc.2007.05.004},
mrnumber = {2436790},
zbl = {1140.35550},
language = {en},
url = {https://www.numdam.org/articles/10.1016/j.anihpc.2007.05.004/}
}
TY - JOUR AU - Shvydkoy, Roman AU - Friedlander, Susan TI - The unstable spectrum of the Navier-Stokes operator in the limit of vanishing viscosity JO - Annales de l'I.H.P. Analyse non linéaire PY - 2008 SP - 713 EP - 724 VL - 25 IS - 4 PB - Elsevier UR - https://www.numdam.org/articles/10.1016/j.anihpc.2007.05.004/ DO - 10.1016/j.anihpc.2007.05.004 LA - en ID - AIHPC_2008__25_4_713_0 ER -
%0 Journal Article %A Shvydkoy, Roman %A Friedlander, Susan %T The unstable spectrum of the Navier-Stokes operator in the limit of vanishing viscosity %J Annales de l'I.H.P. Analyse non linéaire %D 2008 %P 713-724 %V 25 %N 4 %I Elsevier %U https://www.numdam.org/articles/10.1016/j.anihpc.2007.05.004/ %R 10.1016/j.anihpc.2007.05.004 %G en %F AIHPC_2008__25_4_713_0
Shvydkoy, Roman; Friedlander, Susan. The unstable spectrum of the Navier-Stokes operator in the limit of vanishing viscosity. Annales de l'I.H.P. Analyse non linéaire, Tome 25 (2008) no. 4, pp. 713-724. doi: 10.1016/j.anihpc.2007.05.004
[1] , , Evolution Semigroups in Dynamical Systems and Differential Equations, American Mathematical Society, Providence, RI, 1999, MR 2001e:47068. | Zbl | MR
[2] , , , First order pseudodifferential operators on the torus: Normal forms, diophantine phenomena and global hypoellipticity, Ann. Univ. Ferrara, Nuova Ser., Sez. VII 41 (1996) 51-64. | Zbl | MR
[3] , , , Nonlinear instability for the Navier-Stokes equations, Commun. Math. Phys. 264 (2006) 335-347. | MR
[4] , , Localized instabilities in fluids, in: Handbook of Mathematical Fluid Dynamics, vol. II, North-Holland, Amsterdam, 2003, pp. 289-354, MR MR1984155 (2004g:76072). | MR
[5] , Semigroups of Linear Operators and Applications, The Clarendon Press Oxford University Press, New York, 1985, MR 87c:47056. | Zbl | MR
[6] , Nonlinear instability of ideal plane flows, Int. Math. Res. Not. 41 (2004) 2147-2178, MR MR2078852. | Zbl | MR
[7] , , A sufficient condition for instability in the limit of vanishing dissipation, J. Math. Anal. Appl. 221 (2) (1998) 544-558, MR MR1621750 (99g:76065). | Zbl | MR
[8] , The mathematical problem of hydrodynamic stability, J. Math. Mech. 19 (1969/1970) 817-979, MR MR0261182 (41 #5798). | Zbl | MR
[9] , Cocycles and Mañe sequences with an application to ideal fluids, J. Diff. Eq. 229 (2006) 49-62. | Zbl | MR
[10] , The essential spectrum of advective equations, Commun. Math. Phys. 265 (2006) 507-545. | Zbl | MR
[11] , Navier-Stokes Equations, AMS Chelsea Publishing, Providence, RI, 2001, Theory and Numerical Analysis, Reprint of the 1984 edition. MR MR1846644 (2002j:76001). | Zbl | MR
[12] , Spectrum of small oscillations of an ideal fluid and Lyapunov exponents, J. Math. Pures Appl. (9) 75 (6) (1996) 531-557, MR 97k:35203. | Zbl | MR
[13] , , Nonlinear instability in two dimensional ideal fluids: the case of a dominant eigenvalue, Comm. Math. Phys. 243 (2) (2003) 261-273, MR MR2021907 (2004k:76055). | Zbl | MR
[14] , , Dynamo theory methods for hydrodynamic stability, J. Math. Pures Appl. (9) 72 (2) (1993) 145-180, MR 95a:76036. | Zbl | MR
[15] , An introduction to Pseudo-Differential Operators, World Scientific Publishing Co. Inc., Teaneck, NJ, 1991, MR MR1100930 (92b:47083). | Zbl | MR
[16] , The Linearization Method in Hydrodynamical Stability Theory, Translations of Mathematical Monographs, vol. 74, American Mathematical Society, Providence, RI, 1989, Translated from the Russian by J.R. Schulenberger. MR MR1003607 (90h:76001). | Zbl | MR
Cité par Sources :





