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Global Small Solutions to a Complex Fluid Model in Three Dimensional

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Abstract

In this paper, we provide a much simplified proof of the main result in Lin and Zhang (Commun Pure Appl Math 67: 531–580, 2014) concerning the global existence and uniqueness of smooth solutions to the Cauchy problem for a three dimensional incompressible complex fluid model under the assumption that the initial data are close to some equilibrium states. Besides the classical energy method, the interpolating inequalities and the algebraic structure of the equations coming from the incompressibility of the fluid are crucial in our arguments. We combine the energy estimates with the L ∞ estimates for time slices to deduce the key L 1 in time estimates. The latter is responsible for the global in time existence.

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Authors and Affiliations

  1. Courant Institute, New York University, New York, NY, 10012, USA

    Fanghua Lin

  2. Department of Mathematics, Zhejiang University, Hangzhou, 310027, China

    Ting Zhang

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  1. Fanghua Lin
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  2. Ting Zhang
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Correspondence to Ting Zhang.

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Communicated by V. Šverák

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Lin, F., Zhang, T. Global Small Solutions to a Complex Fluid Model in Three Dimensional. Arch Rational Mech Anal 216, 905–920 (2015). https://doi.org/10.1007/s00205-014-0822-1

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  • DOI: https://doi.org/10.1007/s00205-014-0822-1

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