Existence of global L∞L∞ solutions to a generalized n×nn×n hyperbolic system of quadratic type

In this paper, we give the existence of global L∞L∞ bounded entropy solutions for the Cauchy problem of a generalized n×nn×n hyperbolic system of quadratic type. The main difficulty lies in establishing some compactness estimates of the viscosity solutions because the system has been generalized from 2×22×2 to n×nn×n and some linearly degenerate characteristic fields emerged. We obtain the existence of the global weak solutions using the compensated compactness method coupled with the construction of entropy–entropy flux and BV estimates on viscosity solutions.