Remark on the Rate of Decay of Higher Order Derivatives for Solutions to the Navier-Stokes Equations in Rn

Journal of Functional Analysis

Volumn 172, Issue 1, 2000, Pages 1-18

  Oliver, Marcel ^a   Titi, Edriss S ^b  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b University of California at Irvine   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0002458011     PISSN: 00221236     EISSN: None     Source Type: Journal    
DOI: 10.1006/jfan.1999.3550     Document Type: Article

References (19)

1. Bona J. L., Demengel F., Promislow K. S. Fourier splitting and dissipation of nonlinear dispersive waves. Proc. Roy. Soc. Edinburgh Sect. A. 129:1999;477-502.
2. Choi W., Camassa R. Weakly nonlinear internal waves in a two-fluid system. J. Fluid Mech. 313:1996;83-103.
3. Cao C., Rammaha M., Titi E. S. The Navier-Stokes equations of the rotating 2-D sphere: Gevrey regularity and asymptotic degrees of freedom. Z. Angew. Math. Phys. 50:1999;341-360.
4. Ferrari A. B., Titi E. S. Gevrey regularity of solutions of a class of analytic nonlinear parabolic equations. Comm. Partial Differential Equations. 23:1998;1-16.
5. Foias C., Saut J.-C. Asymptotic behavior, as t→+∞, of solutions of Navier-Stokes equations and nonlinear spectral manifolds. Indiana Univ. Math. J. 33:1984;459-477.
6. Foias C., Temam R. Gevrey class regularity for the solutions of the Navier-Stokes equations. J. Funct. Anal. 87:1989;359-369.
7. John F. Partial Differential Equations. 1982;Springer-Verlag, New York.
8. n. Math. Z. 192:1986;135-148.
9. m, with applications to weak solutions. Math. Z. 187:1984;471-480.
10. p. J. Funct. Anal. 152:1998;447-466.
11. Levermore C. D., Oliver M. The complex Ginzburg-Landau equation as a model problem. Lectures in Applied Mathematics. 1996;Amer. Math. Soc. Providence. p. 141-190.
12. 2 decay for weak solutions of the Navier-Stokes equations. Arch. Rational Mech. Anal. 88:1985;209-222.
13. Schonbek M. Large time behavior of solutions to the Navier-Stokes equations. Comm. Partial Differential Equations. 11:1986;733-763.
14. Schonbek M. Lower bounds of rates of decay for solutions to the Navier-Stokes equations. J. Amer. Math. Soc. 4:1991;423-449.
15. Schonbek M. Asymptotic behavior of solutions to the three-dimensional Navier-Stokes equations. Indiana Univ. Math. J. 41:1992;809-823.
16. m spaces. Comm. Partial Differential Equations. 20:1995;103-117.
17. Schonbek M. E., Schonbek T. P., Süli E. Large-time behaviour of solutions to the magnetohydrodynamics equations. Math. Ann. 304:1996;717-756.
18. Schonbek M., Wiegner M. On the decay of higher-order norms of the solutions of Navier-Stokes equations. Proc. Roy Soc. Edinburgh Sect. A. 126:1996;677-685.
19. n. J. London Math. Soc. (2). 35:1987;303-313.