Boltzmann equation

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The Boltzmann equation is given by ([1] Eq 1 Chap. IX)

\[\frac{\partial f_i}{\partial t} = - {\mathbf u}_i \cdot \frac{\partial f_i}{\partial {\mathbf r}} - {\mathbf F}_i \cdot \frac{\partial f_i}{\partial {\mathbf u}_i } + \sum_j C(f_i,f_j) \]

where \(\) is an external force and the function C() represents binary collisions.

[edit] Solution

Recently Gressman and Strain [2] have provided a proof of global existence and rapid decay to equilibrium of classical solutions to the Boltzmann equation.

[edit] See also

[edit] References

  1. Sybren R. De Groot and Peter Mazur "Non-Equilibrium Thermodynamics", Dover Publications
  2. Philip T. Gressman and Robert M. Strain "Global classical solutions of the Boltzmann equation with long-range interactions", Proceedings of the National Academy of Sciences of the United States of America 107 pp. 5744-5749 (2010)
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