Linear instability implies nonlinear instability for various types of viscous boundary layers
Annales de l'I.H.P. Analyse non linéaire, Volume 20 (2003) no. 1, pp. 87-106.
@article{AIHPC_2003__20_1_87_0,
author = {Desjardins, B. and Grenier, E.},
title = {Linear instability implies nonlinear instability for various types of viscous boundary layers},
journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
pages = {87--106},
publisher = {Elsevier},
volume = {20},
number = {1},
year = {2003},
zbl = {01901028},
mrnumber = {1958163},
language = {en},
url = {http://www.numdam.org/item/AIHPC_2003__20_1_87_0/}
}
TY  - JOUR
AU  - Desjardins, B.
AU  - Grenier, E.
TI  - Linear instability implies nonlinear instability for various types of viscous boundary layers
JO  - Annales de l'I.H.P. Analyse non linéaire
PY  - 2003
DA  - 2003///
SP  - 87
EP  - 106
VL  - 20
IS  - 1
PB  - Elsevier
UR  - http://www.numdam.org/item/AIHPC_2003__20_1_87_0/
UR  - https://zbmath.org/?q=an%3A01901028
UR  - https://www.ams.org/mathscinet-getitem?mr=1958163
LA  - en
ID  - AIHPC_2003__20_1_87_0
ER  - 
%0 Journal Article
%A Desjardins, B.
%A Grenier, E.
%T Linear instability implies nonlinear instability for various types of viscous boundary layers
%J Annales de l'I.H.P. Analyse non linéaire
%D 2003
%P 87-106
%V 20
%N 1
%I Elsevier
%G en
%F AIHPC_2003__20_1_87_0
Desjardins, B.; Grenier, E. Linear instability implies nonlinear instability for various types of viscous boundary layers. Annales de l'I.H.P. Analyse non linéaire, Volume 20 (2003) no. 1, pp. 87-106. http://www.numdam.org/item/AIHPC_2003__20_1_87_0/

[1] Desjardins B., Grenier E., Reynolds.m a package to compute critical Reynolds numbers, 1998 , http://www.dmi.ens.fr/equipes/edp/Reynolds/reynolds.html.

[2] Dormy E., Desjardins B., Grenier E., Stability of mixed Ekman-Hartmann boundary layers, Nonlinearity 12 (2) (1999) 181-199. | MR | Zbl

[3] Dormy E., Desjardins B., Grenier E., Instability of Ekman-Hartmann boundary layers, with application to the fluid flow near the core-mantle boundary, Physics of the Earth and Planetary Interiors 123 (2001) 15-26.

[4] Friedlander S., Strauss W., Vishik M., Nonlinear instability in an ideal fluid, Ann. Inst. H. Poincaré Anal. Non Linéaire 14 (1997) 187-209. | Numdam | MR | Zbl

[5] Gisclon M., Serre D., Study of boundary conditions for a strictly hyperbolic system via parabolic approximation, C. R. Acad. Sci. Paris Ser. I Math. 319 (4) (1994) 377-382. | MR | Zbl

[6] Greenspan H.P., The Theory of Rotating Fluids, Cambridge Monographs on Mechanics and Applied Mathematics, 1969. | Zbl

[7] Grenier E., On the nonlinear instability of Euler and Prandtl equations, Comm. Pure Appl. Math. 53 (2000) 1067-1091. | MR | Zbl

[8] Grenier E., Guès O., Boundary layers for viscous perturbations of noncharacteristic quasilinear hyperbolic problems, J. Differential Equations 143 (1) (1998) 110-146. | MR | Zbl

[9] Grenier E., Masmoudi N., Ekman layers of rotating fluids, the case of well prepared initial data, Comm. Partial Differential Equations 22 (1997) 953-975. | MR | Zbl

[10] Guo Y., Strauss W., Instability of periodic BGK equilibria, Comm. Pure Appl. Math. 48 (1995) 861-894. | MR | Zbl

[11] Guo Y., Strauss W., Nonlinear instability of double-humped equilibria, Ann. Inst. H. Poincaré Anal. Non Linéaire 12 (1995) 339-352. | Numdam | MR | Zbl

[12] Henry D., Geometric Theory of Semilinear Parabolic Equations, Lecture Notes in Mathematics, 840, Springer, Berlin, 1981. | MR | Zbl

[13] Iooss G., Nielsen H.B., True H., Bifurcation of the stationary Ekman flow into a stable periodic flow, Arch. Rational Mech. Anal. 68 (3) (1978) 227-256. | MR | Zbl

[14] Lilly D.K., On the instability of the Ekman boundary layer, J. Atmos. Sci. 23 (1966) 481-494.

[15] Majda A., Compressible Fluid Flows Systems of Conservation Laws in Several Variables, Appl. Math. Sci., 53, Springer, Berlin, 1984. | MR | Zbl

[16] Serre D., L1 -stability of travelling waves in scalar conservation laws, Exp. No. VIII, 13 pp., Semin. Equ. Dériv. Partielles, Ecole Polytech., Palaiseau, 1999. | Numdam | MR | Zbl

[17] Serre D., Systèmes de lois de conservations, I et II, Diderot Editeur, Paris, 1996. | MR

[18] Shizuta Y., On the classical solutions of the Boltzmann equation, Comm. Pure Appl. Math. 36 (1983) 705-754. | MR | Zbl

[19] Vidav I., Spectra of perturbed semigroups with applications to transport theory, J. Math. Anal. Appl. 30 (1970) 264-279. | MR | Zbl

[20] Yudovitch V.I., Non-stationary flow of a perfect non-viscous fluid, Zh. Vych. Math. 3 (1963) 1032-1066.