Boltzmann equation

The Boltzmann equation is given by ( 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 ${\displaystyle }$ 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)