Boltzmann equation - Revision history

Carl McBride: /* References */ Added a publication

2017-06-20T09:30:53Z

References: Added a publication

← Older revision		Revision as of 11:30, 20 June 2017
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	==References==		==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]]

Carl McBride: Added a recent publication

2010-05-19T10:00:00Z

Added a recent publication

← Older revision		Revision as of 12:00, 19 May 2010
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	{{Stub-general}}		{{Stub-general}}
	The '''Boltzmann equation''' is given by (~~Ref~~.1 Eq 1 Chap. IX)		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==
	~~#[http:~~/~~/store.doverpublications.com/0486647412.html Sybren R. De Groot and Peter Mazur "Non-Equilibrium Thermodynamics", Dover Publications]~~		<references/>
	[[category: non-equilibrium thermodynamics]]		[[category: non-equilibrium thermodynamics]]

Nice and Tidy at 10:34, 27 September 2007

2007-09-27T10:34:32Z

← Older revision		Revision as of 12:34, 27 September 2007
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			{{Stub-general}}
	The '''Boltzmann equation''' is given by (Ref.1 Eq 1 Chap. IX)		The '''Boltzmann equation''' is given by (Ref.1 Eq 1 Chap. IX)

Carl McBride: New page: The '''Boltzmann equation''' is given by (Ref.1 Eq 1 Chap. IX) : $\frac{\partial f_i}{\partial t} = - {\mathbf u}_i \cdot \frac{\partial f_i}{\partial {\mathbf r}} - {\mathbf F}_i \cd...$

2007-08-22T10:17:12Z

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...

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 \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.
==See also==
*[[H-theorem]]
==References==
#[http://store.doverpublications.com/0486647412.html Sybren R. De Groot and Peter Mazur "Non-Equilibrium Thermodynamics", Dover Publications]
[[category: non-equilibrium thermodynamics]]

Boltzmann equation - Revision history

Carl McBride: /* References */ Added a publication

Carl McBride: Added a recent publication

Nice and Tidy at 10:34, 27 September 2007

Carl McBride: New page: The '''Boltzmann equation''' is given by (Ref.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 \cd...

Carl McBride: New page: The '''Boltzmann equation''' is given by (Ref.1 Eq 1 Chap. IX) : $\frac{\partial f_i}{\partial t} = - {\mathbf u}_i \cdot \frac{\partial f_i}{\partial {\mathbf r}} - {\mathbf F}_i \cd...$