<abstract xmlns="http://www.w3.org/1999/xhtml"> In this paper we study the Cauchy problem of the Fractional Navier-Stokes equations in critical Fourier-Besov-Morrey spaces FṄsp, λ,q(ℝ3) with <inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/mjpaa_2017.3.1.2.jpg"></inline-graphic>. By making use of the Fourier localization method and the Littlewood-Paley theory as in [6] and [21], we get global well-posedness result with small initial data belonging to <inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/mjpaa_2017.3.1.3.jpg"></inline-graphic>. The space FṄsp,λ,q(ℝ3) covers the classical spaces Ḃsq and FḂsp,q(ℝ3) (cf [7],[3], [19], [22]...). The result of this paper extends the works of [6] and [21].</abstract>

In this paper we study the Cauchy problem of the Fractional Navier-Stokes equations in critical Fourier-Besov-Morrey spaces FṄsp, λ,q(ℝ3) with . By making use of the Fourier localization method and the Littlewood-Paley theory as in [6] and [21], we get global well-posedness result with small initial data belonging to . The space FṄsp,λ,q(ℝ3) covers the classical spaces Ḃsq and FḂsp,q(ℝ3) (cf [7],[3], [19], [22]...). The result of this paper extends the works of [6] and [21].

Global Well-Posedness for Fractional Navier-Stokes Equations in critical Fourier-Besov-Morrey Spaces

Moroccan Journal of Pure and Applied Analysis

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

In this paper we study the Cauchy problem of the Fractional Navier-Stokes equations in critical Fourier-Besov-Morrey spaces FṄsp, λ,q(ℝ3) with . By making use...

Global Well-Posedness for Fractional Navier-Stokes Equations in critical Fourier-Besov-Morrey Spaces

Published Online: Aug 01, 2017

Page range: 1 - 13

Received: Sep 20, 2015

Accepted: Aug 10, 2016

DOI: https://doi.org/10.1515/mjpaa-2017-0001

Keywords
Navier-Stokes Equations, global well-posedness, Fourier-Besov- Morrey space

© 2017

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Global Well-Posedness for Fractional Navier-Stokes Equations in critical Fourier-Besov-Morrey Spaces

Published Online: Aug 01, 2017

Page range: 1 - 13

Received: Sep 20, 2015

Accepted: Aug 10, 2016

DOI: https://doi.org/10.1515/mjpaa-2017-0001

KeywordsNavier-Stokes Equations, global well-posedness, Fourier-Besov- Morrey space

© 2017

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Keywords
Navier-Stokes Equations, global well-posedness, Fourier-Besov- Morrey space