The motion of rarefied gases for uniform shear flow at the kinetic level is governed by the spatially homogeneous Boltzmann equation with a deformation force. In this talk, I will report our recent study on the corresponding Cauchy problem with initial data of finite mass and energy for the collision kernel in case of hard potentials. We prove the global existence and large time behavior of solutions provided that the force strength is small enough. In particular, we make a rigorous justification of the uniform-in-time asymptotic expansion of solutions up to order 2 under a homoenergetic self-similar scaling that can capture the increase of temperature when time tends to infinity. This is a joint work with Prof. Renjun Duan.

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