Kinetic shear flow governed by the Boltzmann equation

For a rarefied gas, a uniform shear flow is characterized at a macroscopic level as a state where the horizontal velocity is linear along its normal direction while the density and temperature remain spatially uniform. Due to the shearing motion that induces the viscous heat, the total energy and hence temperature monotonically increase in time. It is more fundamental to understand the change of energy under the effect of shear forces at the kinetic level where the gas motion is governed by the nonlinear Boltzmann equation. In this context, the state is defined as the one that is spatially homogeneous when the velocities of particles are referred to a Lagrangian frame moving with the given macro hearing velocity. In the talk I will present recent results on uniform shear flow via the Boltzmann equation.