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On the global well-posedness of strong dynamics of incompressible nematic liquid crystals in \({\mathbb{R}^N}\)

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Abstract

We consider the motion of a viscous incompressible liquid crystal flow in the N-dimensional whole space. We prove the global well-posedness of strong solutions for small initial data by combining the maximal \({L_p-L_q}\) regularities and \({L_p-L_q}\) decay properties of solutions for the Stokes equations and heat equations. As a result, we also proved the decay properties of the solutions to the nonlinear equations.

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Authors and Affiliations

  1. Department of Mathematics, University of California Santa Cruz, Santa Cruz, CA, USA

    Maria Schonbek

  2. Department of Mathematics, Research Institute of Science and Engineering, Waseda University, Ohkubo 3-4-1, Shinjuku-ku, Tokyo, 169-8555, Japan

    Yoshihiro Shibata

Authors
  1. Maria Schonbek
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  2. Yoshihiro Shibata
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Correspondence to Yoshihiro Shibata.

Additional information

We gratefully dedicate this article to our good friend and wonderfulmathematician, Professor Dr. Jan Prüss, on the occasion of his 65th birthday.

M. Schonbek: Partially supported by Top Global University Project.

Y. Shibata: Partially supported by Top Global University Project and JSPS Grant-in-aid for Scientific Research (S) # 24224004.

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Schonbek, M., Shibata, Y. On the global well-posedness of strong dynamics of incompressible nematic liquid crystals in \({\mathbb{R}^N}\) . J. Evol. Equ. 17, 537–550 (2017). https://doi.org/10.1007/s00028-016-0358-y

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