The unstable spectrum of the surface quasi-geostrophic equation

Journal of Mathematical Fluid Mechanics

Volumn 7, Issue SUPPL., 2005, Pages

  Friedlander, Susan ^a   Shvydkoy, Roman ^a  

^a UNIVERSITY OF ILLINOIS AT CHICAGO   (United States)

Author keywords

Eigenvalues; Essential spectrum; Euler equation; Surface quasi geostrophic equation

Indexed keywords

EIGENVALUES AND EIGENFUNCTIONS; FOURIER TRANSFORMS; MATHEMATICAL OPERATORS; SPECTRUM ANALYSIS; STEADY FLOW; THEOREM PROVING;

ESSENTIAL SPECTRUM; EULER EQUATIONS; FRONTOGENESIS; SURFACE QUASI-GEOSTOPHIC EQUATIONS;

FLUID DYNAMICS;

FLUID DYNAMICS;

EID: 17144427012     PISSN: 14226928     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00021-004-0129-3     Document Type: Article

References (21)

1. P. CONSTANTIN, D. CORDOBA and J. Wu, On the critical dissipative quasi-geostrophic equation, Indiana Univ. Math. J. 50 (2001), Special Issue, Dedicated to Professors Ciprian Foias and Roger Temam, 97-107, (Bloomington, IN, 2000). MR 2002h:35246
2. P. CONSTANTIN, A. J. MAJDA and E. TABAK, Formation of strong fronts in the 2-D quasigeostrophic thermal active scalar, Nonlinearity 7 (1994), no. 6, 1495-1533. MR 95i:76107
3. DIEGO CORDOBA, On the geometry of solutions of the quasi-geostrophic and Euler equations, Proc. Nat. Acad. Sci. U.S.A. 94 (1997), no. 24, 12769-12770. MR 98g:35166
4. DIEGO CORDOBA, Nonexistence of simple hyperbolic blow-up for the quasi-geostrophic equation, Ann. of Math. (2) 148 (1998), no. 3, 1135-1152.
5. DIEGO CORDOBA and CHARLES FEFFERMAN, Growth of solutions for QG and 2D Euler equations, J. Amer. Math. Soc. 15 (2002), no. 3, 665-670 (electronic).
6. LAWRENCE C. EVANS, Partial differential equations, American Mathematical Society, Providence, RI, 1998.
7. SUSAN FRIEDLANDER, On vortex tube stretching and instabilities in an inviscid fluid, J. Math. Fluid Mech. 4 (2002), no. 1, 30-44. MR 1 891 073
8. SUSAN FRIEDLANDER, WALTER STRAUSS and MISHA VISHIK, Nonlinear instability in an ideal fluid, Ann. Inst. H. Poincaré Anal. Non Linéaire 14 (1997), no. 2, 187-209.
9. SUSAN FRIEDLANDER and MISHA VISHIK, Instability criteria for steady flows of a perfect fluid, Chaos 2 (1992), no. 3, 455-460.
10. SUSAN FRIEDLANDER, MISHA VISHIK and VICTOR YUDOVICH, Unstable eigenvalues associated with inviscid fluid flows, J. Math. Fluid Mech. 2 (2000), 365-380. MR 2001m:76009
11. ISAAC M. HELD, RAYMOND T. PIERREHUMBERT, STEPHEN T. GARNER and KYLE L. SWANSON, Surface quasi-geostrophic dynamics, J. Fluid Mech. 282 (1995), 1-20. MR 951:76017
12. L. D. MEŠALKIN and JA. G. SINAǏ, Investigation of the stability of a stationary solution of a system of equations for the plane movement of an incompressible viscous liquid, J. Appl. Math. Mech. 25 (1961), 1700-1705. MR 25 #871
13. ROGER D. NUSSBAUM, The radius of the essential spectrum, Duke Math. J. 37 (1970), 473-478. MR 41 #9028
14. JOSEPH PEDLOSKY, Geophysical fluid dynamics, New York, Springer-Verlag, 1987.
15. MICHAEL RENARDY, On the linear stability of hyperbolic PDEs and viscoelastic flows, Z. Angew. Math. Phys. 45 (1994), no. 6, 854-865. MR 95i:35195
16. RICK SALMON, Lectures on geophysical fluid dynamics, Oxford University Press, New York, 1998. MR 2002d:86001
17. ROMAN SHVYDKOY, A new proof of stability criterion for small perturbations of an ideal fluid (preprint).
18. ROMAN SHVYDKOY and SUSAN FRIEDLANDER, On recent developments in the spectral problem for linearized Euler equation (to appear in Contemp. Math., Nonlinear Partial Differential and Related Analysis).
19. ROMAN SHVYDKOY and YURI LATUSHKIN, Essential spectrum of the linearized 2D Euler equation and Lyapunov-Oseledets exponents (to appear in J. Math. Fluid Mech.).
20. ROMAN SHVYDKOY and YURI LATUSHKIN, The essential spectrum of the linearized 2D Euler operator is a vertical band, Contemp. Math. 327 (2003), 299-304.
21. JIAHONG WU, The 2D dissipative quasi-geostrophic equation, Appl. Math. Lett. 15 (2002), no. 8, 925-930. MR 2004a:35177