Abstract：In this paper， the moment estimate for the homogeneous Boltzmann equation without cut-off for hard potentials is discussed. In 1994， Desvillettes showed that any order moment exists in positive time as long as any moment of order is higher than two initially under hard potentials with angular cut-off[1]. In 1997， Wennberg also proved the same conclusion when relaxing the initial condition to the finiteness of second order[2]. In this paper， their previous results can be improved by extending the moment estimates from the cut off case to the non cut off case， under second moments on the initial datum. The main difficulty is that how to cancel the singularity from the collision kernel. Inspired by the work in [3]， the collision kernel is split into two parts and the Taylor expansion is used to cancel the singularity.
孟 飞. 齐次Boltzmann方程在非角截断及硬势情形下的矩估计[J]. 华中师范大学学报(自然科学版), 2018, 52(6): 768-772.
MENG Fei. Moment estimates for the homogeneous Boltzmann equation for hard potentials without cut-off. journal1, 2018, 52(6): 768-772.
2018, Vol. 52 
