Boltzmann equation: Difference between revisions
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Carl McBride (talk | contribs) (New page: The '''Boltzmann equation''' is given by (Ref.1 Eq 1 Chap. IX) :<math>\frac{\partial f_i}{\partial t} = - {\mathbf u}_i \cdot \frac{\partial f_i}{\partial {\mathbf r}} - {\mathbf F}_i \cd...) |
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The '''Boltzmann equation''' is given by ( | {{Stub-general}} | ||
The '''Boltzmann equation''' is given by (<ref>[http://store.doverpublications.com/0486647412.html Sybren R. De Groot and Peter Mazur "Non-Equilibrium Thermodynamics", Dover Publications]</ref> Eq 1 Chap. IX) | |||
:<math>\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) </math> | :<math>\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) </math> | ||
where <math></math> is an external force and the function C() represents binary collisions. | where <math></math> is an external force and the function C() represents binary collisions. | ||
==Solution== | |||
Recently Gressman and Strain <ref>[http://dx.doi.org/10.1073/pnas.1001185107 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)]</ref> have provided a proof of global existence and rapid decay to equilibrium of classical solutions to the Boltzmann equation. | |||
==See also== | ==See also== | ||
*[[H-theorem]] | *[[H-theorem]] | ||
==References== | ==References== | ||
<references/> | |||
;Related reading | |||
*[http://dx.doi.org/10.1007/s00222-004-0389-9 L. Desvillettes and Cédric Villani "On the trend to global equilibrium for spatially inhomogeneous kinetic systems: The Boltzmann equation", Inventiones mathematicae '''159''' pp. 245-316 (2005)] | |||
[[category: non-equilibrium thermodynamics]] | [[category: non-equilibrium thermodynamics]] | ||
Latest revision as of 11:30, 20 June 2017
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The Boltzmann equation is given by ([1] Eq 1 Chap. IX)
where is an external force and the function C() represents binary collisions.
Solution[edit]
Recently Gressman and Strain [2] have provided a proof of global existence and rapid decay to equilibrium of classical solutions to the Boltzmann equation.
See also[edit]
References[edit]
- ↑ Sybren R. De Groot and Peter Mazur "Non-Equilibrium Thermodynamics", Dover Publications
- ↑ 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)
- Related reading