363 research outputs found
Well-posedness for the heat flow of biharmonic maps with rough initial data
This paper establish the local (or global, resp.) well-posedness of the heat
flow of biharmonic maps from to a compact Riemannian manifold without
boundary with small local BMO (or BMO, resp.) norms.Comment: 24 page
On uniqueness of heat flow of harmonic maps
In this paper, we establish the uniqueness of heat flow of harmonic maps into
(N, h) that have sufficiently small renormalized energies, provided that N is
either a unit sphere or a compact Riemannian homogeneous manifold
without boundary. For such a class of solutions, we also establish the
convexity property of the Dirichlet energy for and the unique
limit property at time infinity. As a corollary, the uniqueness is shown for
heat flow of harmonic maps into any compact Riemannian manifold N without
boundary whose gradients belong to for and satisfying
the Serrin's condition.Comment: 24 pages. Two errors of proof of lemma 2.3 have been fixe
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