[物理学与PDEs]第2章第2节 粘性流体力学方程组 2.6 一维粘性热传导流体动力学方程组

一维粘性热传导流体动力学方程组: $$\beex \bea \cfrac{\p\rho}{\p t}+\cfrac{\p }{\p x}(\rho u)&=0,\\ \cfrac{\p u}{\p t}+u\cfrac{\p u}{\p x} +\cfrac{1}{\rho}\cfrac{\p p}{\p x} -\cfrac{1}{\rho}\cfrac{\p }{\p x}\sez{\sex{\cfrac{4\mu}{3}+\mu'}\cfrac{\p u}{\p x}}&=F,\\ \rho \cfrac{\p e}{\p t} +\rho u\cfrac{\p e}{\p x} +p\cfrac{\p u}{\p x} -\sex{\cfrac{4\mu}{3}+\mu'}\sex{\cfrac{\p u}{\p x}}^2 &=\cfrac{\p}{\p x}\sex{\kappa\cfrac{\p T}{\p x}}. \eea \eeex$$ 此也是拟线性双曲-抛物耦合方程组.