Some Bounds on the Number of Determining Nodes for Weak Solutions of the Navier-stokes Equations

  title={Some Bounds on the Number of Determining Nodes for Weak Solutions of the Navier-stokes Equations},
  author={Michael Holst},
Abstract. We derive new upper bounds on the dimension of the determining set for weak solutions of the Navier-Stokes equations. Our results extend the recent bounds due to Jones and Titi in three ways. First, the bounds are derived under the minimal H-regularity required to define a weak solution of the Navier-Stokes equations. Second, the new bounds are valid for arbitrary polyhedral domains, whereas previous results were derived for the unit square. Third, our results hold also in the three… CONTINUE READING

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