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 l o c q ( [ 0 , ∞ ) ) L^q_{loc}([0,\infty )) for some q > 1 q>1 we establish global existence of a solution with a mean-field that is in general unbounded but in L r ( 0 , T ) L^r(0,T) for some r > 1 r>1 that depends on the coefficients in the model.