演講公告
新聞標題： ( 2012-02-22 )
演講主題：Boundary singularity for Boltzmann equation
主講人：陳逸昆 博士
演講日期：2012年2月23日(星期四) 上午10:30 –11:30
演講地點：(光復校區) 科學一館307室
摘要內容：
有關主講人：
陳逸昆 博士
Ph.D. in Mathematics, University of Maryland
中央研究院數學研究所博士後
研究興趣為Kinetic Theorem, PDE, Analysis
講題：Boundary singularity for Boltzmann equation
Abstract：
We consider the thermal transpiration problem in the kinetic theory, which can be modeled by the linearized Boltzmann equation. It is well-known in WKB model and computations that there is a logarithmic singularity for the fluid velocity around the solid boundary. The goal of this paper is to confirm this basic phenomenon for linearized Boltzmann equation for sufficiently large Knudsen number. To construct a Maxwellianlike solution, we use an iterated scheme, with the ”gain” part of the collision operator as a source. The scheme yields an explicit leading term. The remaining converging terms are estimated through a refined pointwise estimate and Maxwellian upper bound for the gain part. With this explicitly constructed solution, we are able to characterize the singularity on around the boundary. Our analysis is motivated by the previous studies of asymptotic and computational analysis. Numerical data supporting the analysis are also provided.
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