Nonlinear instability of ideal plane flows

International Mathematics Research Notices

Volumn , Issue 41, 2004, Pages 2147-2178

  Lin, Zhiwu ^a  

^a NEW YORK UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 4644372005     PISSN: 10737928     EISSN: None     Source Type: Journal    
DOI: 10.1155/s107379280414018x     Document Type: Article

References (26)

1. C. Bardos, Y. Guo, and W. A. Strauss, Stable and unstable ideal plane flows, Chinese Ann. Math. Ser. B 23 (2002), no. 2, 149-164.
2. M. P. do Carmo, Differential Geometry of Curves and Surfaces, Prentice-Hall, New Jersey, 1976.
3. P. G. Drazin and L. N. Howard, Hydrodynamic stability of parallel flow of an inviscid fluid, Adv. in Appl. Math. 9 (1966), 1-89.
4. P. G. Drazin and W. H. Reid, Hydrodynamic Stability, Cambridge Monographs on Mechanics and Applied Mathematics, Cambridge University Press, Cambridge, 1981.
5. K. S. Eckhoff, On stability for symmetric hyperbolic systems. I, J. Differential Equations 40 (1981), no. 1, 94-115.
6. S. Friedlander, W. A. Strauss, and M. M. Vishik, Nonlinear instability in an ideal fluid, Ann. Inst. H. Poincaré Anal. Non Linéaire 14 (1997), no. 2, 187-209.
7. -, Robustness of instability for the two-dimensional Euler equations, SIAM J. Math. Anal. 30 (1999), no. 6, 1343-1354.
8. S. Friedlander and M. M. Vishik, Instability criteria for the flow of an inviscid incompressible fluid, Phys. Rev. Lett. 66 (1991), no. 17, 2204-2206.
9. G. P. Galdi, An Introduction to the Mathematical Theory of the Navier-Stokes Equations. Vol. I. Linearized Steady Problems, Springer Tracts in Natural Philosophy, vol. 38, Springer-Verlag, New York, 1994.
10. E. Grenier, On the nonlinear instability of Euler and Prandtl equations, Comm. Pure Appl. Math. 53 (2000), no. 9, 1067-1091.
11. Y. Guo and W. A. Strauss, Instability of periodic BGK equilibria, Comm. Pure Appl. Math. 48 (1995), no. 8, 861-894.
12. -, Relativistic unstable periodic BGK waves, Comput. Appl. Math. 18 (1999), no. 1, 87-122.
13. A. Lifschitz and E. Hameiri, Local stability conditions in fluid dynamics, Phys. Fluids A 3 (1991), no. 11, 2644-2651.
14. Z. Lin, Instability of some ideal planeflows, SIAM J. Math. Anal. 35 (2003), no. 2, 318-356.
15. -, Nonlinear instability of periodic waves for Vlasov-Poisson system, to appear in Comm. Pure Appl. Math.
16. -, Some stability and instability criteria for ideal plane flows, to appear in Comm. Math. Phys.
17. -, Some recent results on instability of ideal plane flows, submitted to Proceedings of Northwestern PDE conference.
18. C. Marchioro and M. Pulvirenti, Mathematical Theory of incompressible Nonviscous Fluids, Applied Mathematical Sciences, vol. 96, Springer-Verlag, New York, 1994.
19. M. Mu and Y.-H. Wu, Arnol'd nonlinear stability theorems and their application to the atmosphere and oceans, Surveys in Geophysics 22 (2001), no. 4, 383-426.
20. J. Pedlosky, Geophysical Fluid Dynamics, 2nd ed., Springer-Verlag, New York, 1987.
21. L. Rayleigh, On the stability or instability of certain fluid motions, Proc. London Math. Soc. 9 (1880), 57-70.
22. J. Shatah and W. A. Strauss, Spectral condition for instability, Nonlinear PDE's, Dynamics and Continuum Physics (South Hadley, MA, 1998), Contemp. Math., vol. 255, American Mathematical Society, Rhode Island, 2000, pp. 189-198.
23. R. Shvidkoy and Y. Latushkin, The essential spectrum of the linearized 2D Euler operator is a vertical band, Advances in Differential Equations and Mathematical Physics (Birmingham, AL, 2002), Contemp. Math., vol. 327, American Mathematical Society, Rhode Island, 2003, pp. 299-304.
24. G. E. Swaters, Introduction to Hamiltonian Fluid Dynamics and Stability Theory, Chapman & Hall/CRC Monographs and Surveys in Pure and Applied Mathematics, vol. 102, Chapman & Hall/CRC, Florida, 2000.
25. P. Tabeling, Two-dimensional turbulence: a physicist approach, Phys. Rep. 362 (2002), no. 1, 1-62.
26. M. M. Vishik and S. Friedlander, Nonlinear instability in two dimensional ideal fluids: the case of a dominant eigenvalue, Comm. Math. Phys. 243 (2003), no. 2, 261-273.