Long time decay to the Lei–Lin solution of 3D Navier–Stokes equations

Abstract

In this paper we prove, if u ∈ C([0, ∞), X −1 (R 3 )) is global solution of 3D Navier-Stokes equations, then u(t) X −1 decays to zero as time goes to infinity. Fourier analysis and standard techniques are used.

Blow‐up of the maximal solution to 3D Boussinesq system in Lei‐Lin‐Gevrey spaces

“…It is worthwhile to emphasize that recently the study of Navier‐Stokes equation and other related topics received extensive attention in the framework of Lei‐Lin space, see, for example, previous studies . Especially, in Benhamed, the author proved global well‐posedness and blow‐up criterion for the periodic quasi‐geostrophic equations in Lei‐Lin‐Gevrey spaces.…”

“…One of the serious difficulties when working within the Lei‐Lin space is the fact that this space is not included in the L 2 space and then we have not the classical Leray energy estimate, which is very useful in fluid mechanic theory. To overcome this hard difficulty, as is an interpolation space between Leray space and , s ≥ 3/2 introduced in Benameur and Benameur and Benhamed, we split the spectrum of the initial data into low frequencies that lie simultaneously in the Lei‐Lin‐Gevrey and Leray spaces, and as small as needed high frequencies that belong to the Lei‐Lin‐Gevrey space. For the first, the Leray theory will do the job.…”

Global well-posedness and decay results to 3D generalized viscous magnetohydrodynamic equations

“…Before proving the theorem, we need the following lemma which plays a key role in proving our main result. 1 2 ≤ α ≤ 1, then the following inequality holds…”

Well‐posedness of a 1D transport equation with nonlocal velocity in the Lei–Lin space

“…This paper is partially motivated by the recent progress made by Benameur , Benameur and Benhamed on the classical quasi‐geostrophic equation. We consider the global well‐posedness for the Cauchy problem in space, which was introduced by Lei and Lin in .…”