Transition to turbulence, small disturbances, and sensitivity analysis II: The Navier-Stokes equations

Journal of Mathematical Analysis and Applications

Volumn 337, Issue 2, 2008, Pages 1442-1456

  Singler, John R ^a  

^a Oregon State University   (United States)

Author keywords

Fr chet differentiability; Navier Stokes equations; Nonnormality; Semigroup theory; Sensitivity analysis; Sensitivity equations; Small disturbances; Transition to turbulence

Indexed keywords

EID: 34548614731     PISSN: 0022247X     EISSN: 10960813     Source Type: Journal    
DOI: 10.1016/j.jmaa.2007.03.094     Document Type: Article

References (27)

1. Drazin P.G. Introduction to Hydrodynamic Stability (2002), Cambridge Univ. Press, Cambridge
2. Boberg L., and Brosa U. Onset of turbulence in a pipe. Z. Naturforsch. A 43 8-9 (1988) 697-726
3. Butler K.M., and Farrell B.F. Three-dimensional optimal perturbations in viscous shear flow. Phys. Fluids A 4 8 (1992) 1637-1650
4. Gustavsson L.H. Energy growth of three-dimensional disturbances in plane Poiseuille flow. J. Fluid Mech. 224 (1991) 241-260
5. Reddy S.C., and Henningson D.S. Energy growth in viscous channel flows. J. Fluid Mech. 252 (1993) 209-238
6. Farrell B.F., and Ioannou P.J. Stochastic forcing of the linearized Navier-Stokes equations. Phys. Fluids A 5 11 (1993) 2600-2609
7. Bamieh B., and Dahleh M. Energy amplification in channel flows with stochastic excitation. Phys. Fluids 13 11 (2001) 3258-3269
8. J.R. Singler, Transition to turbulence, small disturbances, and sensitivity analysis I: A motivating problem, J. Math. Anal. Appl., submitted for publication
9. Temam R. Infinite-Dimensional Dynamical Systems in Mechanics and Physics (1997), Springer-Verlag, Berlin
10. Henry D. Geometric Theory of Semilinear Parabolic Equations (1981), Springer-Verlag, New York
11. Deuring P., and von Wahl W. Strong solutions of the Navier-Stokes system in Lipschitz bounded domains. Math. Nachr. 171 (1995) 111-148
12. Fujita H., and Kato T. On the Navier-Stokes initial value problem. I. Arch. Ration. Mech. Anal. 16 (1964) 269-315
13. Sritharan S.S. Invariant Manifold Theory for Hydrodynamic Transition (1990), Longman Scientific & Technical, Harlow, Essex, UK
14. Temam R. Navier-Stokes Equations: Theory and Numerical Analysis (2001), Amer. Math. Soc., Providence, RI
15. Miklavčič M. Applied Functional Analysis and Partial Differential Equations (1998), World Scientific, Singapore
16. Bona J.L., Sun S.M., and Zhang B.-Y. A nonhomogeneous boundary-value problem for the Korteweg-de Vries equation posed on a finite domain. Comm. Partial Differential Equations 28 7-8 (2003) 1391-1436
17. Zeidler E. Nonlinear Functional Analysis and Its Applications I, Fixed-Point Theorems (1986), Springer-Verlag, New York
18. Kreiss G., and Kreiss H.-O. Convergence to steady state of solutions of Burgers' equation. Appl. Numer. Math. 2 (1986) 161-179
19. Schmid P.J., and Henningson D.S. Stability and Transition in Shear Flows (2001), Springer-Verlag, New York
20. Trefethen L.N., Trefethen A.E., Reddy S.C., and Driscoll T.A. Hydrodynamic stability without eigenvalues. Science 261 (1993) 578-584
21. Drazin P.G., and Reid W.H. Hydrodynamic Stability (1981), Cambridge Univ. Press, New York
22. Trefethen L.N., and Embree M. Spectra and Pseudospectra: The Behavior of Nonnormal Matrices and Operators (2005), Princeton Univ. Press
23. Sloane N.J.A. The On-Line Encyclopedia of Integer Sequences. published electronically at (2006). http://www.research.att.com/~njas/sequences/
24. Daners D., and Koch Medina P. Abstract Evolution Equations, Periodic Problems and Applications (1992), Longman Scientific & Technical
25. Barbu V., Lasiecka I., and Triggiani R. Boundary stabilization of Navier-Stokes equations. Mem. Amer. Math. Soc. 181 (2006) No. 852
26. Barbu V., and Triggiani R. Internal stabilization of Navier-Stokes equations with finite dimensional controllers. Indiana Univ. Math. J. 53 5 (2004) 1443-1494
27. Raymond J.-P. Feedback boundary stabilization of the two-dimensional Navier-Stokes equations. SIAM J. Control Optim. 45 3 (2006) 790-828