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Stationary solutions to the Boltzmann equation in the hydrodynamic limit

  • Date March 3, 2016
  • Hour 3 pm
  • Room GSSI Main Lecture Hall
  • Speaker Raffaele Esposito (University of L'Aquila - MEMOCS)

ABSTRACT

While the Cauchy problem for the Boltzmann equation is widely studied, much less is known on the stationary boundary value problem, in particular in the hydrodynamic limit. Using a new L^2-L^\infty approach and new regularity-gain procedure, we prove that, near the global equilibrium, there is a unique positive solution to the stationary Boltzmann equation converging to the stationary solution to th incompressible Navier-Stokes-Fourier system. Moreover the solution is exponentially stable for small initial perturbations.