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On the singular set and the uniqueness of weak solutions of the Navier-Stokes equations

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Abstract

We study regularity properties of weak solutions of the eqns. of Navier-Stokes which are in L∞((O,T),Ln(Ω)) or in LP((O,T),Ln(Ω)) for some p≧2. We prove also that L∞((O,T), Ln(Ω)) is a uniqueness class for weak solutions. Moreover we give a generalization of Serrin's uniqueness result.

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Authors and Affiliations

  1. Fachbereich Mathematik-Informatik der Universität-Gesamthochschule Paderborn, Warburger Str. 100, D 4790, Paderborn

    Hermann Sohr

  2. Lehrstuhl für Angewandte Mathematik, Universität Bayreuth, Postfach 3008, D 8580, Bayreuth

    Wolf von Wahl

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  1. Hermann Sohr
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  2. Wolf von Wahl
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Sohr, H., von Wahl, W. On the singular set and the uniqueness of weak solutions of the Navier-Stokes equations. Manuscripta Math 49, 27–59 (1984). https://doi.org/10.1007/BF01174870

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