On Hydrodynamic Equations at the Limit of Infinitely Many Molecules
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We show that the weak convergence of point measures and (2 + ∈)-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-rescaling 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.
KeywordsProbability Measure Boltzmann Equation Momentum Equation Weak Convergence Hydrodynamic Equation
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