In this paper, we study the existence of global entropy solutions for the Cauchy problem of the extended river flow system with a friction α(x) depending on the space variable x. First, under the boundedness of , we apply the viscosity-flux approximation method coupled with the maximum principle to obtain the a priori L ∞ estimates for the approximation solutions. Second, we prove the pointwise convergence of the approximation solutions by using the compactness framework from the compensated compactness theory. Finally, as a by-product, we obtain the existence of global solutions for isentropic gas flow in the Laval nozzle with friction.

中文翻译：

---

具有摩擦的等熵气流全局解的存在性

在本文中，我们研究了具有取决于空间变量 x 的摩擦力 α(x) 的扩展河流水流系统的柯西问题的全局熵解的存在性。首先，在 的有界下，我们应用粘度-通量近似方法与最大值原理相结合，以获得近似解的先验 L ∞ 估计。其次，我们通过使用补偿紧致理论的紧致框架证明了近似解的逐点收敛。最后，作为副产品，我们获得了具有摩擦力的拉瓦尔喷嘴中等熵气流的全局解的存在性。