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Journal of University of Chinese Academy of Sciences ›› 2023, Vol. 40 ›› Issue (2): 145-154.DOI: 10.7523/j.ucas.2021.0065

• Research Articles •     Next Articles

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

MIN Dezai, WU Gang, YAO Zhuoya   

  1. School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
  • Received:2021-03-08 Revised:2021-04-21 Online:2023-03-15

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 F˙^p,q4α3p(R3). Making use of Fourier localization method and Banach fixed point theorem, we proved that if p>35α, 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=35αq∈[35α65α].

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

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