A note on lower bounds of decay rates for solutions to the Navier-Stokes equations in the norms of Besov spaces

作者：Skalak Zdenek^*

来源：Nonlinear Analysis-Theory Methods & Applications, 2014, 97: 228-233.

DOI：10.1016/j.na.2013.11.007

• Navier-Stokes equations
• Lower bounds of decay
• Energy concentration
• Besov spaces

We study the lower bounds of decay rates for turbulent solutions to the Navier-Stokes equations in the norms of Besov spaces. We focus on solutions satisfying 0 < lim inft ->infinity 8 t(gamma) broken vertical bar broken vertical bar u(t)broken vertical bar broken vertical bar <= lim sup(t)-> t broken vertical bar broken vertical bar u(t)broken vertical bar broken vertical bar < infinity for some gamma epsilon (0, 5/4] and prove among others that such solutions, measured in the norm of the Besov space. B-2,infinity(-gamma) 2,8, are estimated for large times from below by some positive constant. These estimates stem from sufficiently fast rate of large time energy concentration in low frequencies occurring in the studied solutions. Our results have simple proofs and improve and extend substantially the results published by Miyakawa (2002) and by Schonbek and Wiegner (1996).

• 出版日期2014-3