Preprint 2004-042

Global Solutions to the Boltzmann Equation with External Forces

Seiji Ukai, Tong Yang, and Huijiang Zhao

Abstract: For the Boltzmann equation with an external potential force depending only on the space variables, there is a family of stationary solutions which are local Maxwellians with space dependent density, zero velocity and constant temperature. In this paper, we will study the nonlinear stability of these stationary solutions by using energy method. The analysis combines the analytic techniques used for the conservation laws using the fluid-type system derived from the Boltzmann equation, cf. [14], and the dissipative effects on the fluid and non-fluid components of the Boltzmann equation through the celebrated H-theorem. To our knowledge, this is the first result on the global classical solutions to the Boltzmann equation with external force and non-trivial large time behavior in the whole space.

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Seiji Ukai, <>
Tong Yang, <>
Huijiang Zhao, <>
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<> September 3 2004.

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