Cooling Process for Inelastic Boltzmann Equations for Hard Spheres, Part I: The Cauchy Problem

@article{Mischler2006CoolingPF,
  title={Cooling Process for Inelastic Boltzmann Equations for Hard Spheres, Part I: The Cauchy Problem},
  author={St{\'e}phane Mischler and Cl{\'e}ment Mouhot and Mariano Rodriguez Ricard},
  journal={Journal of Statistical Physics},
  year={2006},
  volume={124},
  pages={655-702}
}
We develop the Cauchy theory of the spatially homogeneous inelastic Boltzmann equation for hard spheres, for a general form of collision rate which includes in particular variable restitution coefficients depending on the kinetic energy and the relative velocity as well as the sticky particles model. We prove (local in time) non-concentration estimates in Orlicz spaces, from which we deduce weak stability and existence theorem. Strong stability together with uniqueness and instantaneous… CONTINUE READING

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