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Blow-up Solutions Appearing in the Vorticity Dynamics with Linear Strain

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Abstract

We consider a model equation for 3D vorticity dynamics of incompressible viscous fluid proposed by K. Ohkitani and the second author of the present paper. We prove that a solution blows up in finite time if the \( L^1 \)-norm of the initial vorticity is greater than the viscosity.

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Authors and Affiliations

  1. Dept. of Computer Science, University of Electro-Communications, Chofu, 182-8585, Japan

    K.-I. Nakamura

  2. Research Institute for Mathematical Sciences, Kyoto University, Kyoto, 606-8502, Japan

    H. Okamoto

  3. Dept. of Math., Faculty of Sci. and Tech., Tokyo University of Science, 2641 Yamazaki, Noda-shi, Chiba, 278-8510, Japan

    H. Yagisita

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  1. K.-I. Nakamura
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  2. H. Okamoto
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  3. H. Yagisita
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Nakamura, KI., Okamoto, H. & Yagisita, H. Blow-up Solutions Appearing in the Vorticity Dynamics with Linear Strain. J. math. fluid mech. 6, 157–168 (2004). https://doi.org/10.1007/s00021-003-0087-1

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  • DOI: https://doi.org/10.1007/s00021-003-0087-1

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