On the regularization of the LSW model of coarsening

The LSW model is a kinetic model, formulated by Lifshitz, Slyozov and Wagner around 1960, This model describes the evolution of a set of crystals whose shape is approximately spherical and whose average radius grows like the power t^(1/3). The main factor that drives the growth of the average set of the crystals is the tendency of the system to reduce the interfacial area, and the main limiting factor for the speed of growth is the diffusion of material in the intersticial space between the crystals. In recent year there were several results that provide a more rigorous basis for the LSW theory of coarsening. In particular it has been established by B. Niethammer and R. L. Pego that the dynamics of the solutions of the LSW model depend very sensitively on the initial distribution of particle radii. During this talk I will review some of these results and I will describe some of the mechanisms that have been suggested as possible regularizing mechanisms for the LSW dynamics. In particular I will describe how to compute corrections to the LSW dynamics due to the stochastic fluctuations in the particle densities as well as the role played by the encounters between the particles.