We present a number of exact solutions to the linearised Grad equations for non-equilibrium rarefied gas flows and heat flows. The solutions include the flow and pressure fields associated to a point force placed in a rarefied gas flow close to a no-slip boundary and the temperature field for a point heat source placed in a heat flow close to a temperature jump boundary. We also derive the solution of the unsteady Grad equations in one dimension with a time-dependent point heat source term and the Grad analogue of the rotlet, a well-known singularity of Stokes flow which corresponds to a point torque.

中文翻译：

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微型气体流的新的精确解决方案

对于非平衡稀薄气体流和热流，我们为线性化Grad方程提供了许多精确解。解决方案包括与置于无滑移边界附近的稀薄气流中的点力相关的流场和压力场，以及位于靠近温度跃变边界的热流中的点热源的温度场。我们还使用与时间有关的点热源项和小转子的Grad类似物（与点转矩相对应的众所周知的Stokes流奇异性），在一维中求解非稳态Grad方程的解。