The large-time energy concentration in solutions to the Navier-Stokes equations with nonzero external forces

0395206 - ÚH 2014 RIV US eng J - Článek v odborném periodiku
Skalák, Zdeněk
The large-time energy concentration in solutions to the Navier-Stokes equations with nonzero external forces.
Journal of Mathematical Analysis and Applications. Roč. 402, č. 1 (2013), s. 147-156. ISSN 0022-247X. E-ISSN 1096-0813
Institucionální podpora: RVO:67985874
Klíčová slova: the Navier-Stokes equations * external forces * energy concentration in frequency space
Kód oboru RIV: BK - Mechanika tekutin
Impakt faktor: 1.119, rok: 2013
http://www.sciencedirect.com/science/article/pii/S0022247X13000152

It is known that the turbulent solutions to the unforced Navier-Stokes equations exhibit a large-time energy concentration in the frequency space. If we suppose the existence of a nonzero time dependent external force f is an element of L-1((0, infinity); L-sigma(2)) in the equations, the situation is more complicated. It is possible to construct simple examples of solutions, in which the energy is asymptotically distributed over the entire spectrum of the Stokes operator. Further, we will show as the main result of this paper that there still exist wide classes of initial conditions and external forces yielding solutions with the large-time energy concentration analogical to the situation in the unforced Navier-Stokes equations. We will also show that the frequency spectrum of the solution does not generally relate to the frequency spectrum of the external force.
Trvalý link: http://hdl.handle.net/11104/0231142