Well-posedness of 3D incompressible generalized Navier-Stokes system in Fourier-Triebel-Lizorkin spaces

doi:10.7523/j.ucas.2021.0065

Abstract

Abstract: In this paper, we consider the Cauchy problem for the 3D incompressible generalized Navier-Stokes system and study the well-posedness in critical Fourier-Triebel-Lizorkin spaces ${\hat{\dot{F}}}_{p, q}^{4 - α - \frac{3}{p}}$ ( $R^{3}$ ). Making use of Fourier localization method and Banach fixed point theorem, we proved that if $p > \frac{3}{5 - α}$ , q ≥ 1, the system is locally well-posed for large initial data as well as global well-posed for small initial data. Also we established same result for $p = \frac{3}{5 - α}$ ，q∈[ $\frac{3}{5 - α}$ ， $\frac{6}{5 - α}$ ].

Key words: Navier-Stokes system, Fourier-Triebel-Lizorkin spaces, global well-posedness, local well-posedness

CLC Number:

O175.2

MIN Dezai, WU Gang, YAO Zhuoya. Well-posedness of 3D incompressible generalized Navier-Stokes system in Fourier-Triebel-Lizorkin spaces[J]. Journal of University of Chinese Academy of Sciences, 2023, 40(2): 145-154.

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