Boltzmann equation

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

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \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 ${\displaystyle }$ is an external force and the function C() represents binary collisions.

Solution

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

See also

• H-theorem

References

Related reading

• 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)