Previous |  Up |  Next

Article

Keywords:
decay rates; Navier-Stokes equations
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 \[ \Vert u(t) \Vert \ge (t+1)^{-\frac{n+4}{2}}. \]
References:
[1] A. Carpio: Large-time behavior in incompressible Navier-Stokes equations. SIAM J. Math. Anal. 27 (1996), 449–475. MR 1377483 | Zbl 0845.76019
[2] Y. Fujigaki, T. Miyakawa: Asymptotic profiles of nonstationary incompressible NavierStokes flows in ${\mathbb{R}}^n$. Preprint, Kobe University, 2000.
[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
[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
[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
[6] M. E. Schonbek: Large time behaviour of solutions to the Navier-Stokes equations. Commun. Partial Diff. Eq. 11 (1986), 733–763. MR 0837929 | Zbl 0607.35071
[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. MR 1103459 | Zbl 0739.35070
[8] M. E. Schonbek: Asymptotic behavior of solutions to the three-dimensional Navier-Stokes equations. Indiana Univ. Math. J. 41 (1992), 809–823. MR 1189912 | Zbl 0759.35036
[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. MR 1727469 | Zbl 0954.35131
[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
Partner of
EuDML logo