國立清華大學 數學系

Abstract：
The Boltzmann equation is composed of free transport part and collision part, which describes the particle dynamics, where the collision term is given by an integral operator. Our primary contribution is to establish the moment loss-free Hardy-Littlewood-Sobolev type bilinear estimates for the gain term of collision operator under Grad cut-off hard sphere, hard potential, and Maxwell molecular models. The 3-dimensional case was resolved by Professor Jin-Cheng Jiang, and my work is to extend the result to all dimension greater or equal to 2.  An application of our work is that we acn combine our estimates with KT Strichartz estimates, establised by Ovcharov in 2009, to obtain the well-posedness of mild solutions for the gain-term only equation with small initial data.