ON HYDRODYNAMIC EQUATIONS AT THE LIMIT OF INFINITELY MANY MOLECULES

摘要

We show that the weak convergence of point measures and (2 + ε)-moment conditions imply hydrodynamic equations at the limit of infinitely many interacting molecules. The conditions are satisfied whenever the solutions of the classical equations for N interacting molecules obey uniform in N bounds. As an example, we show that this holds when the initial conditions are bounded and the molecule interaction, a certain N-reseating of potentials that include all r~(-p) for 1 ＜ p, is weak enough at the initial time. In this case, the hydrodynamic equations coincide with the macroscopic Maxwell equations. Bibliography: 23 titles.