Existence of solutions to a continuum model for hydrostatics of fluid-saturated granular materials

In this letter, we establish an existence theory for an overdetermined system of nonlinear PDEs describing hydrostatics of fluid-saturated granular materials. Our proof consists of three steps: (i) the conduction of an integrability analysis, (ii) the reduction of the governing system to a singular elliptic PDE, for which the existence of solutions can be obtained via weak-convergence methods, and (iii) the development of an existence theory for the original system.