Hydrodynamical description of one-component weakly coupled plasmas

Starting from the Vlasov-Landau kinetic equation, linearized around the global equilibrium state and assuming the finite dimensional approximation to the non-hydrodynamical subspace, we derive the hydrodynamical equations for a weakly coupled, one-component plasma. Explicit expressions are given for the transport coefficients and frequencies of the hydrodynamical modes. These results describe the influence of the plasma oscillations on the hydrodynamical behaviour of the system. Certain differences are obtained compared with the standard phenomenological approach. Also the real part of the frequency for the plasma mode in our model is in agreement with the Bohm-Gross dispersion relation.