A. Mouton
Submitted.
Links : HAL.
Abstract : The Boltzmann-Nordheim equation, also known as quantum Boltzmann equation, is a kinetic model written in dx * dv + 1 dimensions (dx = 1,2,3, dv = 2,3), which describes a particle cloud that involves some quantum effects. This consideration induces a trilinear collision operator within the model and time relaxation phenomena that are quite different from the usual Boltzmann context. Indeed, besides the maxwellian-like limit profile, we can observe a time relaxation towards a profile that describes a Bose-Einstein condensate or a Fermi-Dirac saturation according to the initial datum definition. In the present paper, we focus on the these limit profiles and there hydrodynamic description by their momenta of order 0,1,2. After introducing these momenta (ρ,q,ε), we exhibit the Euler-like model satisfied by these quantities and we investigate the plane waves that can be considered. Finally, we use these calculations to solve the Riemann problem for dx = 1 and present some numerical results.