| Title:
|
On optimal decay rates for weak solutions to the Navier-Stokes equations in $R^n$ (English) |
| Author:
|
Miyakawa, Tetsuro |
| Author:
|
Schonbek, Maria Elena |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
126 |
| Issue:
|
2 |
| Year:
|
2001 |
| Pages:
|
443-455 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
This paper is concerned with optimal lower bounds of decay rates for solutions to the Navier-Stokes equations in $\mathbb{R}^n$. Necessary and sufficient conditions are given such that the corresponding Navier-Stokes solutions are shown to satisfy the algebraic bound \[ \Vert u(t) \Vert \ge (t+1)^{-\frac{n+4}{2}}. \] (English) |
| Keyword:
|
decay rates |
| Keyword:
|
Navier-Stokes equations |
| MSC:
|
35B40 |
| MSC:
|
35B45 |
| MSC:
|
35D99 |
| MSC:
|
35Q10 |
| MSC:
|
35Q30 |
| MSC:
|
76D05 |
| idZBL:
|
Zbl 0981.35048 |
| idMR:
|
MR1844282 |
| DOI:
|
10.21136/MB.2001.134008 |
| . |
| Date available:
|
2009-09-24T21:52:34Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/134008 |
| . |
| Reference:
|
[1] A. Carpio: Large-time behavior in incompressible Navier-Stokes equations.SIAM J. Math. Anal. 27 (1996), 449–475. Zbl 0845.76019, MR 1377483, 10.1137/S0036141093256782 |
| Reference:
|
[2] Y. Fujigaki, T. Miyakawa: Asymptotic profiles of nonstationary incompressible NavierStokes flows in ${\mathbb{R}}^n$.Preprint, Kobe University, 2000. |
| Reference:
|
[3] R. Kajikiya, T. Miyakawa: On $L^2$ decay of weak solutions of the Navier-Stokes equations in ${\mathbb{R}}^n$.Math. Z. 192 (1986), 135–148. MR 0835398, 10.1007/BF01162027 |
| Reference:
|
[4] T. Miyakawa: Application of Hardy space techniques to the time-decay problem for incompressible Navier-Stokes flows in ${\mathbb{R}}^n$.Funkcial. Ekvac. 41 (1998), 383–434. MR 1676881 |
| Reference:
|
[5] M. E. Schonbek: $L^2$ decay for weak solutions of the Navier-Stokes equations.Arch. Rational Mech. Anal. 88 (1985), 209–222. MR 0775190, 10.1007/BF00752111 |
| Reference:
|
[6] M. E. Schonbek: Large time behaviour of solutions to the Navier-Stokes equations.Commun. Partial Diff. Eq. 11 (1986), 733–763. Zbl 0607.35071, MR 0837929, 10.1080/03605308608820443 |
| Reference:
|
[7] M. E. Schonbek: Lower bounds of rates of decay for solutions to the Navier-Stokes equations.J. Amer. Math. Soc. 4 (1991), 423–449. Zbl 0739.35070, MR 1103459, 10.1090/S0894-0347-1991-1103459-2 |
| Reference:
|
[8] M. E. Schonbek: Asymptotic behavior of solutions to the three-dimensional Navier-Stokes equations.Indiana Univ. Math. J. 41 (1992), 809–823. Zbl 0759.35036, MR 1189912, 10.1512/iumj.1992.41.41042 |
| Reference:
|
[9] M. E. Schonbek: On decay of solutions to the Navier-Stokes equations.Applied Nonlinear Analysis, A. Sequeira, H. Beirao da Veiga, J. H. Videman (eds.), Kluwer/Plenum, New York, 1999, pp. 505–512. Zbl 0954.35131, MR 1727469 |
| Reference:
|
[10] M. Wiegner: Decay results for weak solutions of the Navier-Stokes equations in ${\mathbb{R}}^n$.J. London Math. Soc. 35 (1987), 303–313. MR 0881519 |
| . |
