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NCTS Seminar on Analysis
15:30 - 16:30, July 2, 2018 (Monday)
Room 202, Astronomy-Mathematics Building, NTU
(台灣大學天文數學館 202室)
Pointwise Estimate of the Solution of the Linearized Boltzmann Equation
Haitao Wang (Shanghai Jiao Tong University)


We study the 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 the study. This is a joint work with Yu-Chu Lin and Kung-Chien Wu.


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