caa a22 4500 463171012 CHVBK 20180406164813.0 cr unu---uuuuu 170326e20071201xx s 000 0 eng 10.1007/s00021-006-0222-x doi (NATIONALLICENCE)springer-10.1007/s00021-006-0222-x Skalák Zdeněk Institute of Hydrodynamics, Pod Pat̆ankou 30/5, 166 12, Prague 6, Czech Republic aut Fast Decays of Strong Global Solutions of the Navier-Stokes Equations [Elektronische Daten] [Zdeněk Skalák] Abstract.: In the paper we study the asymptotic dynamics of strong global solutions of the Navier Stokes equations. We are concerned with the question whether or not a strong global solution w can pass through arbitrarily large fast decays. Avoiding results on higher regularity of w used in other papers we prove as the main result that for the case of homogeneous Navier-Stokes equations the answer is negative: If $$\varepsilon \in$$ [0, 1/4) and δ0 > 0, then the quotient $$\|A^{1+\varepsilon}w(t)\|/\|w(t+\delta)\|$$ remains bounded for all t ≥ 0 and δ∈[0, δ0]. This result is not valid for the non-homogeneous case. We present an example of a strong global solution w of the non-homogeneous Navier-Stokes equations, where the exterior force f decreases very quickly to zero for $$t \rightarrow \infty$$ while w passes infinitely often through stages of arbitrarily large fast decays. Nevertheless, we show that for the non-homogeneous case arbitrarily large fast decays (measured in the norm $$\|A^{\beta}.\|)$$ cannot occur at the time t in which the norm $$\|A^{\beta}w(t)\|$$ is greater than a given positive number. Birkhaueser, 2007 Navier-Stokes equations nationallicence strong global solutions nationallicence fast decay of solutions nationallicence asymptotic behavior nationallicence Journal of Mathematical Fluid Mechanics SP Birkhäuser Verlag Basel 9/4(2007-12-01), 565-587 1422-6928 9:4<565 2007 9 21 https://doi.org/10.1007/s00021-006-0222-x text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00021-006-0222-x text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Skalák Zdeněk Institute of Hydrodynamics, Pod Pat̆ankou 30/5, 166 12, Prague 6, Czech Republic aut NATIONALLICENCE 773 0- Journal of Mathematical Fluid Mechanics SP Birkhäuser Verlag Basel 9/4(2007-12-01), 565-587 1422-6928 9:4<565 2007 9 21 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer