J. Nonl. Evol. Equ. Appl. 2021 (6), pp. 119-135, published on December 30, 2021:

Long time decay of the fractional Navier-Stokes equations in Sobolev-Gevery spaces

X. Sun, J. Liu

College of Mathematics and Statistics Northwest Normal University, Lanzhou, 730070, P. R. China

Received on June 3, 2020, revised version on May 10, 2021
Accepted on May 11, 2021

Communicated by Martin Bohner

Abstract.  In this paper, we prove that if u ∈ C([0, ∞), H˙(ℝ3)) is a global solution of 3D fractional Navier-Stokes equations,where H˙ is the Sobolev-Gevery space with parameters a > 0 and α ∈ (2/3, 1], then ║u(t)║H˙(ℝ3) decays to zero as time approaches infinity. Our technique is based on Fourier analysis.
Keywords:fractional Navier-Stokes equations; Long time decay; Sobolev-Gevery spaces.
2010 Mathematics Subject Classification:   Primary 35Q30; Secondary 76B03; 42B37.

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