Crack Opening Models Based on the Exact Solutions of the Navier-Stokes Equations

Abstract

Different approximate crack opening models in a porous stratum are derived, based on a priori representations of the crack size, accurate solutions of motion equations of viscous fluid, approximate expressions of the filtering model in the stratum, and approximate expressions of the theory of elasticity of the stratum. The law of conservation of mass of the fluid in the crack is used to obtain quasilinear parabolic equations, describing the crack opening.