Finite-dimensional global attractor for globally modified Navier–Stokes equations with fractional dissipation
Volume 122 / 2019
Annales Polonici Mathematici 122 (2019), 101-128
MSC: Primary 35K65, 35B40; Secondary 37L30.
DOI: 10.4064/ap180616-29-10
Published online: 23 April 2019
Abstract
The paper deals with the globally modified Navier–Stokes equations with fractional dissipation in a periodic box. The existence, uniqueness and large time behavior of weak solutions are investigated. The existence and some sharp regularity results for the global attractor are established, and an upper bound for its fractal dimension is provided.
