Crossover in coarsening rates for the monopole approximation of the Mullins-Sekerka model with kinetic drag

The Mullins-Sekerka sharp-interface model for phase transitions interpolates between attachment-limited and diffusion-limited kinetics if kinetic drag is included in the Gibbs-Thomson interface condition. Heuristics suggest that the typical length scale of patterns may exhibit a crossover in coarsening rate from l(t) ∼ t1/2 at short times to l(t) ∼ t1/3 at long times. We establish rigorous, universal one-sided bounds on energy decay that partially justify this understanding in the monopole approximation and in the associated LSW mean-field model. Numerical simulations for the LSW model illustrate the crossover behavior. The proofs are based on a method for estimating coarsening rates introduced by Kohn and Otto, and make use of a gradient-flow structure that the monopole approximation inherits from the Mullins-Sekerka model by restricting particle geometry to spheres.