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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.

##### MSC:
 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
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