Duality in Boltzmann Equation and its Applications.

Duality in Boltzmann Equation and its Applications.

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Shih-Hsien Yu, National University of Singapore
Fine Hall 314

In this paper we will survey a quantitative and qualitative development on the Boltzmann equation. This development reveals the dual natures of the Boltzmann equation: The particlelike nature and the fluidlike nature. This dual nature property gives rise to the precise construction of the Green's function for Boltzmann equation around a  global Maxwellian state. With the precise structure of the Green's function, one can implement the Green's function to study various problems such as invariant manifolds for the steady Boltzmann flows, time asymptotic nonlinear stability of Boltzmann shock  layers and Boltzmann boundary layers, Riemann Problem, and bifurcation problem of boundary layer problem, etc.