The global solutions of axisymmetric Navier–Stokes equations with anisotropic initial data

  • Hui ChenEmail author
  • Daoyuan Fang
  • Ting Zhang


Consider the Cauchy problem of incompressible Navier–Stokes equations in three dimension with axisymmetric initial data. If the swirl component satisfies some certain regularity criteria in weighted spaces, the existence of the time-global solution has been proved in our previous work. However, it is more or less evident that the solution is anisotropic in vertical direction (i.e., the direction parallel to the axis of symmetry) and the horizontal directions (in the plane perpendicular to the axis of symmetry). In this paper, we are interested in constructing regularity criteria and time-global solution in anisotropic Lebesgue spaces.


Axisymmetric Navier–Stokes equations Regularity criteria Global solution Anisotropic 

Mathematics Subject Classification

Primary 35Q30 Secondary 76D03 76D05 76N10 



The authors would like to thank the anonymous referee for his (her) careful reading and kind suggestions on the manuscript.


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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.School of ScienceZhejiang University of Science and TechnologyHangzhouPeople’s Republic of China
  2. 2.School of Mathematical SciencesZhejiang UniversityHangzhouPeople’s Republic of China

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