On optimal decay rates for weak solutions to the Navier-Stokes equations in R n

Tetsuro Miyakawa; Maria Elena Schonbek

Mathematica Bohemica (2001)

  • Volume: 126, Issue: 2, page 443-455
  • ISSN: 0862-7959

Abstract

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This paper is concerned with optimal lower bounds of decay rates for solutions to the Navier-Stokes equations in ℝ n . Necessary and sufficient conditions are given such that the corresponding Navier-Stokes solutions are shown to satisfy the algebraic bound ∥ u ( t ) ∥ ≥ ( t + 1 ) - n + 4 2 .

How to cite

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Miyakawa, Tetsuro, and Schonbek, Maria Elena. "On optimal decay rates for weak solutions to the Navier-Stokes equations in $R^n$." Mathematica Bohemica 126.2 (2001): 443-455. <http://eudml.org/doc/248871>.

@article{Miyakawa2001,
abstract = {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 \[ \Vert u(t) \Vert \ge (t+1)^\{-\frac\{n+4\}\{2\}\}. \]},
author = {Miyakawa, Tetsuro, Schonbek, Maria Elena},
journal = {Mathematica Bohemica},
keywords = {decay rates; Navier-Stokes equations; decay rates; Navier-Stokes equations},
language = {eng},
number = {2},
pages = {443-455},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On optimal decay rates for weak solutions to the Navier-Stokes equations in $R^n$},
url = {http://eudml.org/doc/248871},
volume = {126},
year = {2001},
}

TY - JOUR
AU - Miyakawa, Tetsuro
AU - Schonbek, Maria Elena
TI - On optimal decay rates for weak solutions to the Navier-Stokes equations in $R^n$
JO - Mathematica Bohemica
PY - 2001
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 126
IS - 2
SP - 443
EP - 455
AB - 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 \[ \Vert u(t) \Vert \ge (t+1)^{-\frac{n+4}{2}}. \]
LA - eng
KW - decay rates; Navier-Stokes equations; decay rates; Navier-Stokes equations
UR - http://eudml.org/doc/248871
ER -

References

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  8. 10.1512/iumj.1992.41.41042, Indiana Univ. Math. J. 41 (1992), 809–823. (1992) Zbl0759.35036MR1189912DOI10.1512/iumj.1992.41.41042
  9. 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. (1999) Zbl0954.35131MR1727469
  10. Decay results for weak solutions of the Navier-Stokes equations in ℝ n , J. London Math. Soc. 35 (1987), 303–313. (1987) MR0881519

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