GLOBAL WELL-POSEDNESS OF BOLTZMANN-FERMI-DIRAC EQUATION FOR HARD POTENTIAL

. Boltzmann-Fermi-Dirac equation is a modification of classical Boltzmann equation when quantum effects are taken into account in dilute gas dynamics. We consider the well-posedness of Boltzmann-Fermi-Dirac equation for the collision kernel B(|v - v*|, cos 0) given by an inverse power-law repulsive potential. Precisely, B(|v - v*|, cos theta) = |v - v(*)|(2 rho-5 )(sin(rho-3) theta/2 - cos (rho-3 )theta/2)(2) and 1 < p < 3. With this kind of collision kernel, we employ the new estimates of bilinear and trilinear terms in collision integral to obtain the global existence of Boltzmann-Fermi-Dirac equation near equilibrium for 52 < p < 3. The main difficulty comes from the singularity arising from the angular part of B(|v - v(*)|, cos theta).