Journal of Mathematical Sciences

, Volume 205, Issue 2, pp 222–239 | Cite as

On Hydrodynamic Equations at the Limit of Infinitely Many Molecules

  • S. Dostoglou
  • N. C. Jacob
  • Jianfei Xue

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.


Probability Measure Boltzmann Equation Momentum Equation Weak Convergence Hydrodynamic Equation 
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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.University of MissouriColumbiaUSA

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