We consider the Landau equation with Coulomb potentials. We discuss a global existence result close to equilibrium and a short time existence result for general data. In both cases we take initial data in unweighted Lp spaces for p > 3/2. We thus work with the weakest class of initial data that has been considered until now. This is joint work with William Golding (UT Austin) and Maria Gualdani (UT Austin).