Decay and Continuity of the Boltzmann Equation in Bounded Domains

By Yan Guo. 2008

303 citations recorded by the source corpus.

Boundaries occur naturally in kinetic equations, and boundary effects are crucial for dynamics of dilute gases governed by the Boltzmann equation. We develop a mathematical theory to study the time decay and continuity of Boltzmann solutions for four basic types of boundary conditions: in-flow, bounce-back reflection, specular reflection and diffuse reflection. We establish exponential decay in the L∞ norm for hard potentials for general classes of smooth domains near an absolute Maxwellian. Moreover, in convex domains, we also establish continuity for these Boltzmann solutions away from the grazing set at the boundary. Our contribution is based on a new L2 decay theory and its interplay with delicate L∞ decay analysis for the linearized Boltzmann equation in the presence of many repeated interactions with the boundary.

Subfields: Applied Mathematics, Modeling and Simulation

View Paper: https://www.semanticscholar.org/paper/640f6f7b4f7897b3529036cb9f85ae9cc50845b6

How researchers see this paper

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In Applied Mathematics

1. R. Esposito
2. C. Kim
3. Yan Guo
4. R. Marra

In Modeling and Simulation

1. R. Esposito
2. C. Kim
3. Yan Guo
4. R. Marra

Citations in the corpus

• Non-Isothermal Boundary in the Boltzmann Theory and Fourier Law (2013, methodology): “30) given in [22] is based on a delicate contradiction argument because it is difficult to estimate Pf via {I − P}f directly in a L2 setting in the elliptic equation (1.”