Wave structures of the linearized Boltzmann equation in a periodic box
吳恭儉博士University of Cambridge 下午 4:00–5:30 鴻經館 107 室摘要：
We study the wave structures of the linearized Boltzmann equation in a periodic box for non-smooth initial perturbations. The result reveals both the fluid and kinetic aspects of this model. The fluid-like waves are constructed as part of the long-wave expansion in the spectrum of the Fourier mode for the space variable, and the time decay rate of the fluid-like waves depends on the size of the domain. We design a Picard-type iteration for constructing the increasingly regular kinetic-like waves, which are carried by the transport equations and have exponential time decay rate. The iterated averaging lemma plays an important role in
constructing the kinetic-like waves. We also supply some new ideas of this lemma.