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Well-posedness for the heat flow of harmonic maps and the liquid crystal flow with rough initial data. (English) Zbl 1285.35085
Summary: 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\(^{ - 1} \times \) BMO.

35Q35 PDEs in connection with fluid mechanics
35K45 Initial value problems for second-order parabolic systems
35B30 Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs
35K15 Initial value problems for second-order parabolic equations
35K59 Quasilinear parabolic equations
58E20 Harmonic maps, etc.
76A15 Liquid crystals
Full Text: DOI arXiv
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