Linear instability implies nonlinear instability for various types of viscous boundary layers
Annales de l'I.H.P. Analyse non linéaire (2003)
- Volume: 20, Issue: 1, page 87-106
- ISSN: 0294-1449
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topDesjardins, B., and Grenier, E.. "Linear instability implies nonlinear instability for various types of viscous boundary layers." Annales de l'I.H.P. Analyse non linéaire 20.1 (2003): 87-106. <http://eudml.org/doc/78575>.
@article{Desjardins2003,
author = {Desjardins, B., Grenier, E.},
journal = {Annales de l'I.H.P. Analyse non linéaire},
language = {eng},
number = {1},
pages = {87-106},
publisher = {Elsevier},
title = {Linear instability implies nonlinear instability for various types of viscous boundary layers},
url = {http://eudml.org/doc/78575},
volume = {20},
year = {2003},
}
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
PB - Elsevier
VL - 20
IS - 1
SP - 87
EP - 106
LA - eng
UR - http://eudml.org/doc/78575
ER -
References
top- [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, Nonlinearity12 (2) (1999) 181-199. Zbl0939.35151MR1677778
- [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 Interiors123 (2001) 15-26.
- [4] Friedlander S., Strauss W., Vishik M., Nonlinear instability in an ideal fluid, Ann. Inst. H. Poincaré Anal. Non Linéaire14 (1997) 187-209. Zbl0874.76026MR1441392
- [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. Zbl0808.35075MR1289315
- [6] Greenspan H.P., The Theory of Rotating Fluids, Cambridge Monographs on Mechanics and Applied Mathematics, 1969. Zbl0182.28103
- [7] Grenier E., On the nonlinear instability of Euler and Prandtl equations, Comm. Pure Appl. Math.53 (2000) 1067-1091. Zbl1048.35081MR1761409
- [8] Grenier E., Guès O., Boundary layers for viscous perturbations of noncharacteristic quasilinear hyperbolic problems, J. Differential Equations143 (1) (1998) 110-146. Zbl0896.35078MR1604888
- [9] Grenier E., Masmoudi N., Ekman layers of rotating fluids, the case of well prepared initial data, Comm. Partial Differential Equations22 (1997) 953-975. Zbl0880.35093MR1452174
- [10] Guo Y., Strauss W., Instability of periodic BGK equilibria, Comm. Pure Appl. Math.48 (1995) 861-894. Zbl0840.45012MR1361017
- [11] Guo Y., Strauss W., Nonlinear instability of double-humped equilibria, Ann. Inst. H. Poincaré Anal. Non Linéaire12 (1995) 339-352. Zbl0836.35130MR1340268
- [12] Henry D., Geometric Theory of Semilinear Parabolic Equations, Lecture Notes in Mathematics, 840, Springer, Berlin, 1981. Zbl0456.35001MR610244
- [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. Zbl0395.76045MR509226
- [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. Zbl0537.76001MR748308
- [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. Zbl1063.35520MR1721326
- [17] Serre D., Systèmes de lois de conservations, I et II, Diderot Editeur, Paris, 1996. MR1459988
- [18] Shizuta Y., On the classical solutions of the Boltzmann equation, Comm. Pure Appl. Math.36 (1983) 705-754. Zbl0515.35002MR720591
- [19] Vidav I., Spectra of perturbed semigroups with applications to transport theory, J. Math. Anal. Appl.30 (1970) 264-279. Zbl0195.13704MR259662
- [20] Yudovitch V.I., Non-stationary flow of a perfect non-viscous fluid, Zh. Vych. Math.3 (1963) 1032-1066.
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