@article{AIHPC_2003__20_1_87_0, author = {Desjardins, B. and Grenier, Emmanuel}, title = {Linear instability implies nonlinear instability for various types of viscous boundary layers}, journal = {Annales de l'I.H.P. Analyse non lin\'eaire}, volume = {20}, year = {2003}, pages = {87-106}, mrnumber = {1958163}, zbl = {01901028}, language = {en}, url = {http://dml.mathdoc.fr/item/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, Tome 20 (2003) pp. 87-106. http://gdmltest.u-ga.fr/item/AIHPC_2003__20_1_87_0/
[1] Reynolds.m a package to compute critical Reynolds numbers, 1998 , http://www.dmi.ens.fr/equipes/edp/Reynolds/reynolds.html.
, ,[2] Stability of mixed Ekman-Hartmann boundary layers, Nonlinearity 12 (2) (1999) 181-199. | MR 1677778 | Zbl 0939.35151
, , ,[3] 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] Nonlinear instability in an ideal fluid, Ann. Inst. H. Poincaré Anal. Non Linéaire 14 (1997) 187-209. | Numdam | MR 1441392 | Zbl 0874.76026
, , ,[5] 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 1289315 | Zbl 0808.35075
, ,[6] The Theory of Rotating Fluids, Cambridge Monographs on Mechanics and Applied Mathematics, 1969. | Zbl 0182.28103
,[7] On the nonlinear instability of Euler and Prandtl equations, Comm. Pure Appl. Math. 53 (2000) 1067-1091. | MR 1761409 | Zbl 1048.35081
,[8] Boundary layers for viscous perturbations of noncharacteristic quasilinear hyperbolic problems, J. Differential Equations 143 (1) (1998) 110-146. | MR 1604888 | Zbl 0896.35078
, ,[9] Ekman layers of rotating fluids, the case of well prepared initial data, Comm. Partial Differential Equations 22 (1997) 953-975. | MR 1452174 | Zbl 0880.35093
, ,[10] Instability of periodic BGK equilibria, Comm. Pure Appl. Math. 48 (1995) 861-894. | MR 1361017 | Zbl 0840.45012
, ,[11] Nonlinear instability of double-humped equilibria, Ann. Inst. H. Poincaré Anal. Non Linéaire 12 (1995) 339-352. | Numdam | MR 1340268 | Zbl 0836.35130
, ,[12] Geometric Theory of Semilinear Parabolic Equations, Lecture Notes in Mathematics, 840, Springer, Berlin, 1981. | MR 610244 | Zbl 0456.35001
,[13] Bifurcation of the stationary Ekman flow into a stable periodic flow, Arch. Rational Mech. Anal. 68 (3) (1978) 227-256. | MR 509226 | Zbl 0395.76045
, , ,[14] On the instability of the Ekman boundary layer, J. Atmos. Sci. 23 (1966) 481-494.
,[15] Compressible Fluid Flows Systems of Conservation Laws in Several Variables, Appl. Math. Sci., 53, Springer, Berlin, 1984. | MR 748308 | Zbl 0537.76001
,[16] L1 -stability of travelling waves in scalar conservation laws, Exp. No. VIII, 13 pp., Semin. Equ. Dériv. Partielles, Ecole Polytech., Palaiseau, 1999. | Numdam | MR 1721326 | Zbl 1063.35520
,[17] Systèmes de lois de conservations, I et II, Diderot Editeur, Paris, 1996. | MR 1459988
,[18] On the classical solutions of the Boltzmann equation, Comm. Pure Appl. Math. 36 (1983) 705-754. | MR 720591 | Zbl 0515.35002
,[19] Spectra of perturbed semigroups with applications to transport theory, J. Math. Anal. Appl. 30 (1970) 264-279. | MR 259662 | Zbl 0195.13704
,[20] Non-stationary flow of a perfect non-viscous fluid, Zh. Vych. Math. 3 (1963) 1032-1066.
,