國立清華大學 數學系

Abstract: We will introduce two kinds of singular behavior of Boltzmann equation near boundary. First kind is the logarithmic singularity of the macroscopic quantities; the second kind is the logarithmic singularity of the velocity distribution function in molecular velocity. We prove both under the setting of thermal transpiration problem as an canonical example. Finally, we prove the logarithmic singularity of moments (macroscopic quantities) in a general setting. Our theorem holds for the solutions of the Milne and Kramers problems obtained by Bardos-Caflish- Nicolaenko,1986. Our theorem requires the Holder continuity of the boundary data. In particular, it applies to the complete condensation problem for half space. Tea Time: 3:30, R707