caa a22 4500 463171063 CHVBK 20180406164813.0 cr unu---uuuuu 170326e20071201xx s 000 0 eng 10.1007/s00021-005-0211-5 doi (NATIONALLICENCE)springer-10.1007/s00021-005-0211-5 On the Time Decay of the Solutions of the Navier-Stokes System [Elektronische Daten] [Šárka Nečasová, Patrick Rabier] Abstract.: We investigate the relationship between the time decay of the solutions u of the Navier-Stokes system on a bounded open subset of $$\mathbb{R}^{N}$$ and the time decay of the right-hand sides f. In suitable function spaces, we prove that u always inherits at least part of the decay of f, up to exponential, and that the decay properties of u depend only upon the amount and type (e.g., exponential, or power-like) of decay of f. This is done by first making clear what is meant by "type” and "amount” of decay and by next elaborating upon recent abstract results pointing to the fact that, in linear and nonlinear PDEs, the decay of the solutions is often intimately related to the Fredholmness of the differential operator. Birkhaueser, 2006 Navier-Stokes nationallicence Fredholm operator nationallicence exponential decay nationallicence Nečasová Šárka Mathematical Institute of the Czech Academy of Sciences, Žitnà 25, CZ-11567, Prague 1, Czech Republic aut Rabier Patrick Department of Mathematics, University of Pittsburgh, 15260, Pittsburgh, PA, USA aut Journal of Mathematical Fluid Mechanics SP Birkhäuser Verlag Basel 9/4(2007-12-01), 517-532 1422-6928 9:4<517 2007 9 21 https://doi.org/10.1007/s00021-005-0211-5 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00021-005-0211-5 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Nečasová Šárka Mathematical Institute of the Czech Academy of Sciences, Žitnà 25, CZ-11567, Prague 1, Czech Republic aut NATIONALLICENCE 700 1- Rabier Patrick Department of Mathematics, University of Pittsburgh, 15260, Pittsburgh, PA, USA aut NATIONALLICENCE 773 0- Journal of Mathematical Fluid Mechanics SP Birkhäuser Verlag Basel 9/4(2007-12-01), 517-532 1422-6928 9:4<517 2007 9 21 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer