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.
@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},
     publisher = {Elsevier},
     volume = {25},
     number = {4},
     year = {2008},
     doi = {10.1016/j.anihpc.2007.05.004},
     mrnumber = {2436790},
     zbl = {1140.35550},
     language = {en},
     url = {http://archive.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  - http://archive.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 http://archive.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. http://archive.numdam.org/articles/10.1016/j.anihpc.2007.05.004/

[1] Chicone C., Latushkin Y., Evolution Semigroups in Dynamical Systems and Differential Equations, American Mathematical Society, Providence, RI, 1999, MR 2001e:47068. | MR | Zbl

[2] Dickinson D., Gramchev T., Yoshino M., 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. | MR | Zbl

[3] Friedlander S., Pavlović N., Shvydkoy R., Nonlinear instability for the Navier-Stokes equations, Commun. Math. Phys. 264 (2006) 335-347. | MR

[4] Friedlander S., Lipton-Lifschitz A., 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] Goldstein J.A., Semigroups of Linear Operators and Applications, The Clarendon Press Oxford University Press, New York, 1985, MR 87c:47056. | MR | Zbl

[6] Lin Z., Nonlinear instability of ideal plane flows, Int. Math. Res. Not. 41 (2004) 2147-2178, MR MR2078852. | MR | Zbl

[7] Lyashenko A.A., Friedlander S.J., A sufficient condition for instability in the limit of vanishing dissipation, J. Math. Anal. Appl. 221 (2) (1998) 544-558, MR MR1621750 (99g:76065). | MR | Zbl

[8] Sattinger D.H., The mathematical problem of hydrodynamic stability, J. Math. Mech. 19 (1969/1970) 817-979, MR MR0261182 (41 #5798). | MR | Zbl

[9] Shvydkoy R., Cocycles and Mañe sequences with an application to ideal fluids, J. Diff. Eq. 229 (2006) 49-62. | MR | Zbl

[10] Shvydkoy R., The essential spectrum of advective equations, Commun. Math. Phys. 265 (2006) 507-545. | MR | Zbl

[11] Temam R., Navier-Stokes Equations, AMS Chelsea Publishing, Providence, RI, 2001, Theory and Numerical Analysis, Reprint of the 1984 edition. MR MR1846644 (2002j:76001). | MR | Zbl

[12] Vishik M., Spectrum of small oscillations of an ideal fluid and Lyapunov exponents, J. Math. Pures Appl. (9) 75 (6) (1996) 531-557, MR 97k:35203. | MR | Zbl

[13] Vishik M., Friedlander S., 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). | MR | Zbl

[14] Vishik M., Friedlander S., Dynamo theory methods for hydrodynamic stability, J. Math. Pures Appl. (9) 72 (2) (1993) 145-180, MR 95a:76036. | MR | Zbl

[15] Wong M.W., An introduction to Pseudo-Differential Operators, World Scientific Publishing Co. Inc., Teaneck, NJ, 1991, MR MR1100930 (92b:47083). | MR | Zbl

[16] Yudovich V.I., 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). | MR | Zbl

Cité par Sources :