Limits on enstrophy growth for solutions of the three-dimensional Navier-Stokes equations

Indiana University Mathematics Journal

Volumn 57, Issue 6, 2008, Pages 2693-2727

  Lu, Lu ^a   Doering, Charles R ^b  

^a Wachovia Securities   (United States)

^b UNIVERSITY OF MICHIGAN   (United States)

Author keywords

Enstrophy; Fluid dynamics; Navier Stokes equations; Vorticity

Indexed keywords

EID: 59549098973     PISSN: 00222518     EISSN: None     Source Type: Journal    
DOI: 10.1512/iumj.2008.57.3716     Document Type: Article

References (23)

1. R. A. ADAMS, Sobolev spaces, Academic Press, New York, 1975.
2. G.K. BATCHELOR, An introduction to fluid dynamics, Cambridge University Press, Cambridge, 1967.
3. JOHN P. BOYD, Chebyshev and fourier spectrum methods, 2nd, Dover, New York, 2001.
4. C. BASDEVANT, Le modéle de simulation numérique de turbulence bidimensionnelle du l.m.d, Tech. report (1982).
5. C. BASDEVANT, M.O. DEVILLE, P. HALDENWANG, J.-M. LACROIX, J. OUAZZANI, R. PEYRET, P. ORLANDI, and A.T. PATERA, Spectral and finite difference solutions of the burger's equation, Computers and Fluids 14 (1986), 23-41.
6. CHIN-CHOU CHU, CHI-TZUNG WANG, CHIEN-CHENG CHANG, RAY-YU CHANG, and WEN-TYZH CHANG, Head-on collision of two coaxial vortex rings: Experiment and computation, J. Fluid Mech. 296 (1995), 39-71.
7. C.R. DOERING and E.S. TITI, Exponential decay rate of the power spectrum for solutions of the Navier Stokes equations, Phys. Fluids 7 (1995), 1384-1390.
8. CHARLES R. DOERING and J.D. GIBBON, Applied analysis of the navier-stokes equations, Cambridge University Press, Cambridge, U.K., 1995.
9. Y.G. EVTUSHENKO and V.G. ZHADAN, Stable barrier-projection and barrier-Newton methods in nonlinear programming, Optimization Methods and Software 3 (1994), 237-256.
10. C. FOIAS and R. TEMAM, Gevrey class regularity for the solutions of the Navier Stokes equations, J. Funct. Anal. 87 (1989), 359-369.
11. MATTEO FRIGO and STEVEN G. JOHNSON, The design and implementation of fftw3, Proceedings of the IEEE 93 (2005), no. 2), 216-231, http://www.fftw.org+.
12. D.D. LANTERMAN, D.P. LATHROP, B.W. ZEFF, R. MCALLISTER, and R. ROY, Characterizing intense rotation and dissipation in turbulent flows, Chaos 14 (2004).
13. J. LERAY, Essai sur le mourvement d'un liquide visquex emplissant l'espace, Acta Math. 63 (1934), 193-248.
14. LU LU, Bounds on the enstrophy growth rate for solutions of the 3d Navier-Stokes equations, 2006, Ph.D. thesis.
15. L. NIRENBERG, On elliptic partial differential equations, Annali della Scuola Norm. Sup 13 (1959), 115-162.
16. ROGER PEYRET, Spectral methods for incompressible viscous flows, Springer-Verlag, New York, New York, 2002.
17. J.B. ROSEN, The gradient projection method for nonlinear programming. Part i, linear constraints, J. Soc. Indust. Appl. Math. 8 (1960).
18. -, The gradient projection method for nonlinear programming. Part ii, nonlinear constraints, J. Soc. Indust. Appl. Math. 9 (1961).
19. -, Numerical simulation of homogeneous anisotropic turbulence, (Conference Internationale sur les Methodes Numeriques en Dynamique des Fluides, 8th, Aachen, West Germany, June 28-July 2, 1982.) (1982), Research supported by the Direction des Recherches, Etudes et Techniques.
20. X. Q. YANG, S. WANG, and K. L. TEO, A unified gradient flow approach to constrained nonlinear optimization problems, Computational Optimization and Applications 25 (2003), 251-268.
21. K. SHARIFF and A. LEONARD, Vortex rings, Ann. Rev. Fluid Mech. 24 (1992), 235-279.
22. A. VINCENT and M. MENEGUZZI, The spatial structure and statistical properties of homogeneous turbulence, Journal of Fluid Mechanics 225 (1991), 1-20.
23. B.W. ZEFF, D.D. LANTERMAN, R. MCALLISTER, E.J. KOSTELICH R. ROY, and D.P. LATHROP, Measuring intense rotation and dissipation in turbulent flows, Nature 421 (2003), 146-149.