Abstract:

In this paper, we study the weak solutions for the systems of multifluid flows, which includes the system of isentropic gas dynamics in Eulerian coordinates and a system arising from river flows. There are more linearly degenerate fields compared with single-component system, and singularities in these linearly degenerate fields emerge when considering the corresponding vanishing viscosity system. we obtain the existence of global solutions for the system of multifluid flows by analyzing the uniform BV estimates in linearly degenerate fields, coupled with the compensated compactness method and the vanishing viscosity method.

Key words: Multifluid flow, Compensated compactness, Vanishing viscosity method