重力驱动雪崩流运动的二维Savage-Hutter模型的弱解
On weak solutions to the 2D Savage-Hutter model of the motion of a gravity driven avalanche flow
摘要：
我们考虑Savage-Hutter系统，该系统由具有库仑型摩擦项的不可压缩流体的二维深度积分浅水方程组成。利用凸积分的方法，我们证明了相关的初值问题具有无穷多个弱解的任何有限能量的初始数据。另一方面，只要方程组被补充以能量不等式，问题就具有弱-强唯一性。
英文摘要：
We consider the Savage-Hutter system consisting of two-dimensional depth-integrated shallow water equations for the incompressible fluid with the Coulomb-type friction term. Using the method of convex integration we show that the associated initial-value problem possesses infinitely many weak solutions for any finite-energy initial data. On the other hand, the problem enjoys the weak-strong uniqueness property provided the system of equations is supplemented with the energy inequality.
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