On the initial-value problem in the Lifshitz-Slyozov-Wagner theory of Ostwald ripening

The Lifshitz-Slyozov-Wagner (LSW) theory of Ostwald ripening concerns the t ime evolution of the size distribution of a dilute system of particles that evolve by diffusional mass transfer with a common mean field. We prove glo bal existence, uniqueness, and continuous dependence on initial data for me asure-valued solutions with compact support in particle size. These results are established with respect to a natural topology on the space of size di stributions, one given by the Wasserstein metric which measures the smalles t maximum volume change required to rearrange one distribution into another .