Level Sets of the Vorticity and the Stream Function for the 2D Periodic Navier–Stokes Equations with Potential Forces

@inproceedings{Kukavica1996LevelSO,
  title={Level Sets of the Vorticity and the Stream Function for the 2D Periodic Navier–Stokes Equations with Potential Forces},
  author={Igor Kukavica},
  year={1996}
}
Abstract By a result of Foias and Saut, the quotient of the enstrophy and the energy of a solution of the Navier–Stokes equations with potential forces converges to the square root of an eigenvalue Λ k of the Stokes operator. We study the Hausdorff length ( H 1 ) of the level sets of the vorticity and the stream function of solutions. We provide upper bounds for these quantities, and for large t we express them in terms of the corresponding eigenvalue Λ k . 

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