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Well-posedness for the heat flow of harmonic maps and the liquid crystal flow with rough initial data

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Abstract

We investigate the well-posedness of (1) the heat flow of harmonic maps from \({\mathbb R^n}\) to a compact Riemannian manifold N without boundary for initial data in BMO; and (2) the hydrodynamic flow (u, d) of nematic liquid crystals on \({\mathbb R^n}\) for initial data in BMO−1 × BMO.

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Authors and Affiliations

  1. Department of Mathematics, University of Kentucky, Lexington, KY, 40506, USA

    Changyou Wang

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  1. Changyou Wang
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Correspondence to Changyou Wang.

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Communicated by V. Šverák

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Wang, C. Well-posedness for the heat flow of harmonic maps and the liquid crystal flow with rough initial data. Arch Rational Mech Anal 200, 1–19 (2011). https://doi.org/10.1007/s00205-010-0343-5

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  • DOI: https://doi.org/10.1007/s00205-010-0343-5

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