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Quantitative Pointwise Estimate of the Solution of the Linearized Boltzmann Equation

Speaker

Kung-Chien Wu, National Cheng Kung University

Time

2018.01.23 14:00-15:00

Venue

601 Pao Yue-Kong Library

Abstract

We study the quantitative pointwise behavior of the solutions of the linearized Boltzmann equation for hard potentials, Maxwellian molecules and soft potentials, with Grad’s angular cutoff assumption. More precisely, for solutions inside the finite Mach number region, we obtain the pointwise fluid structure for hard potentials and Maxwellian molecules, and optimal time decay in the fluid part and sub-exponential time decay in the non-fluid part for soft potentials. For solutions outside the finite Mach number region, we obtain sub-exponential decay in the space variable. The singular wave estimate, regularization estimate and refined weighted energy estimate play important roles in this paper. This is a joint work with Yu-Chu Lin and Haitao Wang.