We will discuss the coarsening rates for a non-local Cahn-Hilliard equation. The results depend on the exponent s of the underlying kernel and are consistent with the corresponding sharp interfacial limits. For s < 1/2, the limiting dynamics is given by a genuine non-local Mullins-Sekerka dynamics while for s > 1/2, by the classical local version. The approach is based on a work of Kohn and Otto. The key technical lemmas are two inequalities. One is an interpolation inequality that relates the energy (E) and the length scale (L) of the spatial pattern and the other relates their temporal rate of change. This is joint work with Yuan Gao and Tao Luo.
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