| Abstract: |
| In this talk, we will present the existence and long-time behavior of the Boltzmann equation with a deformation matrix $A$, which describes the 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 the well-posedness in the case of hard potentials. In the case where $tr A \geq 0$, we will specifically consider the planar shear flow case and establish the stability of the stationary solution when the collision kernel is limited to the Maxwell molecules. This is a joint work with Prof. Shuangqian Liu, Yating Wang and Xueying Zhang. |
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