In this talk, we will present the existence and long-time behavior of the Boltzmann equation with a deformation matrix A, which describes shear flow. Assuming the shear rate is small, we will study the corresponding Cauchy problem under the cutoff assumption. We will consider two cases: in the case where tr A< 0, we will prove well-posedness for hard potentials. In the case where trA≥0, we will specifically consider the planar shear flow case and establish the stability of the stationary solution when the collision kernel is limited to Maxwell molecules. This is joint work with Prof. Shuangqian Liu, Yating Wang, and Xueying Zhang.