Abstract：

In this talk, we consider the perturbation solution of the Boltzmann equation around a global Maxwellian with a polynomial tail in microscopic velocity. By decomposing the solution into particle-like and fluid-like parts, using the known Green's function, and refining estimates of space-time convolutions, we are able to construct a space-time structure of the solution. However, this decomposition does not respect the conservation law structure, thus our approach is essentially semi-linear and works only for dimension ≥ 3. If time permits, we will also discuss the possibility of a better decomposition. This is a joint work with Yu-Chu Lin and Kung-Chien Wu.

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