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Vorticity and Regularity for Solutions of Initial-boundary Value Problems for the Navier—Stokes Equations

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Hyperbolic Problems and Regularity Questions

Part of the book series: Trends in Mathematics ((TM))

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Abstract

In reference [7], among other side results, we prove that the solution of the evolution Navier—Stokes equations (1.1) under the Navier (or slip) boundary condition (1.2) is necessarily regular if the direction of the vorticity is 1/2-Hölder continuous with respect to the space variables. In this notes we show the main steps in the proof and made some comments on the above problem under the non-slip boundary condition (3.2).

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Author information

Authors and Affiliations

  1. Dipartimento di Matematica Applicata “U. Dini”, Università di Pisa, Via Diotisalvi 2, I-56100, Pisa, Italy

    Hugo Beirão da Veiga

Authors
  1. Hugo Beirão da Veiga
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Editor information

Editors and Affiliations

  1. Dipartimento di Matematica, Università di Ferrara via Machiavelli, 35, I-44100, Ferrara, Italy

    Mariarosaria Padula  & Luisa Zanghirati  & 

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© 2006 Birkhäuser Verlag Basel/Switzerland

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da Veiga, H.B. (2006). Vorticity and Regularity for Solutions of Initial-boundary Value Problems for the Navier—Stokes Equations. In: Padula, M., Zanghirati, L. (eds) Hyperbolic Problems and Regularity Questions. Trends in Mathematics. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-7451-8_5

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