Partial regularity of solutions of the 3-D incompressible Navier-Stokes equations. 23rd Brazilian mathematics colloquium, Rio de Janeiro, Brazil, July 23--27, 2001 (Q2753383)
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scientific article; zbMATH DE number 1668283
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Partial regularity of solutions of the 3-D incompressible Navier-Stokes equations. 23rd Brazilian mathematics colloquium, Rio de Janeiro, Brazil, July 23--27, 2001 |
scientific article; zbMATH DE number 1668283 |
Statements
4 November 2001
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incompressible Navier-Stokes equations
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partial regularity
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Cauchy problem
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zero force function
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Hausdorff dimension of singular set
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weak solution
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Partial regularity of solutions of the 3-D incompressible Navier-Stokes equations. 23rd Brazilian mathematics colloquium, Rio de Janeiro, Brazil, July 23--27, 2001 (English)
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It is a detailed exposition of \textit{L. Caffarelli, R. Kohn}, and \textit{L. Nirenberg}'s paper [Commun. Pure Appl. Math. 35, 771-831 (1982; Zbl 0509.35067)] in a simple case when the Cauchy problem is studied with zero force function. The topic is the improvement of the \textit{V. Scheffer}'s result [Commun. Math. Phys. 73, 1-42 (1980; Zbl 0451.35048)] on the Hausdorff dimension of singular set \(S\) of suitable weak solution. Scheffer proved that \(\mathcal{H}^{5/3}(S)=0\), while Caffarelli, Kohn, and Nirenberg established that \(\mathcal{H}^1 (S)=0.\)
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