Rate of convergence to self-similarity for Smoluchowski's coagulation   equation with constant coefficients
  We show that solutions to Smoluchowski's equation with a constant coagulation kernel and an initial datum with some regularity and exponentially decaying tail converge exponentially fast to a self-similar profile. This convergence holds in a weighted Sobolev norm which implies the L\^2 convergence of derivatives up to a certain order k depending on the regularity of the initial condition. We prove these results through the study of the linearized coagulation equation in self-similar variables, for which we show a spectral gap in a scale of weighted Sobolev spaces. We also take advantage of the fact that the Laplace or Fourier transforms of this equation can be explicitly solved in this case. 
Jos\'e Alfredo Ca\~nizo, St\'ephane Mischler (CEREMADE), Cl\'ement   Mouhot (CEREMADE)