From Boltzmann equation to the incompressible Navier-Stokes-Fourier system with long-range interactions

From Boltzmann equation to the incompressible Navier-Stokes-Fourier system with long-range interactions

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Diogo Arsenio, Courant Institute for Mathematics, NYC
Fine Hall 110

Boltzmann's equation is known to converge, under a certain hydrodynamic regime, to an incompressible Navier-Stokes-Fourier system. It is only recently that the final steps to a mathematically rigorous and complete justification of this hydrodynamic convergence were provided. However, only certain types of intermolecular interactions, still physically unsatisfying, were considered.We establish this hydrodynamic limit for the physically relevant case of long range intermolecular interactions. In this situation, the difficulty comes from the fact that the Boltzmann collision operator exhibits a rather complex nature due to a non-integrable singularity in the collision kernel.