On a singular Lifshitz-Slyozov-Wagner model

We investigate the well-posedness of the classical Lifshitz-Slyozov-Wagner mean-field model for Ostwald ripening with singular coefficients, as they appear, for example in two-dimensional diffusion controlled growth. For Hölder-continuous initial data we prove the existence and uniqueness of a global solution with bounded mean-field. If the data are only in $L^q_{loc}([0,\infty ))$ for some $q>1$ we establish global existence of a solution with a mean-field that is in general unbounded but in $L^r(0,T)$ for some $r>1$ that depends on the coefficients in the model.