Author:
Melo Wilberclay G.,Rocha Nata F.,Costa Natielle dos Santos
Abstract
In this article, we prove the existence of a unique global solution for the critical case of the generalized Navier-Stokes equations in Lei-Lin and Lei-Lin-Gevrey spaces, by assuming that the initial data is small enough. Moreover, we obtain a unique local solution for the subcritical case of this system, for any initial data, in these same spaces. It is important to point out that our main result is obtained by discussing some properties of the solutions for the heat equation with fractional dissipation.
For more information see https://ejde.math.txstate.edu/Volumes/2023/78/abstr.html
Reference37 articles.
1. H. Bae; Existence and analyticity of Lei-Lin solution to the Navier-Stokes equation, Proc. Amer. Math. Soc., 143 (2015), 2887{2892.
2. J. Benameur; On the blow-up criterion of 3D Navier-Stokes equations, J. Math. Anal. Appl., 371 (2010), 719-727.
3. J. Benameur; On the exponential type explosion of Navier-Stokes equations, Nonlinear Anal., 103 (2014), 87-97.
4. J. Benameur; Long time decay to the Lei-Lin solution of 3D Navier-Stokes equations, J. Math. Anal. Appl., 422 (2015), 424-434.
5. J. Benameur, L. Jlali; Long time decay for 3D Navier-Stokes equations in Sobolev-Gevrey spaces, Electron. J. Di erential Equations, (2016), 13 pp.