Improved Liouville theorems for axially symmetric Navier-Stokes equations

@inproceedings{Lei2017ImprovedLT,
  title={Improved Liouville theorems for axially symmetric Navier-Stokes equations},
  author={Zhen Lei and Qi S. Zhang and Na Zhao},
  year={2017}
}
  • Zhen Lei, Qi S. Zhang, Na Zhao
  • Published 2017
  • Mathematics
  • In this paper, we consider the Liouville property for ancient solutions of the incompressible Navier-Stokes equations. In 2D and the 3D axially symmetric case without swirl, we prove sharp Liouville theorems for smooth ancient mild solutions: velocity fields $v$ are constants if vorticity fields satisfy certain condition and $v$ are sublinear with respect to spatial variables, and we also give counterexamples when $v$ are linear with respect to spatial variables. The condition which vorticity… CONTINUE READING

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