Decay of solutions to the three-dimensional generalized Navier–Stokes equations

Article type: Research Article

Authors: Jiu, Quansen^{; *} | Yu, Huan

Affiliations: School of Mathematical Sciences, Capital Normal University, Beijing 100048, China. E-mails: [email protected], [email protected]

Correspondence: [*] Corresponding author. E-mail: [email protected].

Abstract: In this paper, temporal decay estimates for weak solutions to the three dimensional generalized Navier–Stokes equations are established firstly. With these estimates at disposal, algebraic time decay for higher order Sobolev norms of small initial data solutions are obtained. The decay rates are optimal in the sense that they coincide with ones of the corresponding generalized heat equation.

Keywords: generalized Navier–Stokes equations, decay, Fourier-splitting method

DOI: 10.3233/ASY-151307

Journal: Asymptotic Analysis, vol. 94, no. 1-2, pp. 105-124, 2015