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

@inproceedings{Holst1995SomeBO,
  title={Some Bounds on the Number of Determining Nodes for Weak Solutions of the Navier-stokes Equations},
  author={Michael Holst},
  year={1995}
}
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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Showing 1-10 of 11 references

Upper bounds on the number of determining modes, nodes, and volume elements for the Navier- Stokes equations

  • D. Jones, E. Titi
  • Indiana University Mathematics Journal,
  • 1993
Highly Influential
16 Excerpts

On the number of determining nodes for the 2d Navier-Stokes equations

  • D. Jones, E. Titi
  • J. Math. Anal. Appl.,
  • 1992
1 Excerpt

Manifolds, Tensor Analysis, and Applications

  • R. Abraham, J. E. Marsden, T. Ratiu
  • 1988
1 Excerpt

Multi-level Iterative Techniques

  • S. Zhang
  • PhD thesis, Dept. of Mathematics, Pennsylvania…
  • 1988
1 Excerpt

On the dimension of the attractors in two-dimensional turbulence

  • P. Constantin, C. Foias, R. Temam
  • Physica D,
  • 1988
1 Excerpt

Elliptic Problems in Nonsmooth Domains

  • P. Grisvard
  • Pitman Publishing, Marshfield,
  • 1985
1 Excerpt

Functional Analysis I

  • M. Reed, B. Simon
  • 1980
1 Excerpt

Sobolev Spaces

  • R. A. Adams
  • 1978
3 Excerpts

Introductory Real Analysis

  • A. N. Kolmogorov, S. V. Fomin
  • Dover Publications,
  • 1970
1 Excerpt

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