Crack Opening Models Based the Exact Solutions of Navier-Stokes Equations
S. V. Khabirov, S. S. Khabirov
Mavlyutov Institute of Mechanics, Ufa, 450054, Russia
Keywords: раскрытие трещины, уравнение Навье - Стокса, точные решения, квазилинейные параболические уравнения, crack opening, Navier-Stokes equations, exact solutions, quasilinear parabolic 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 momentum of the fluid in the crack is used to obtain quasilinear parabolic equations, describing the crack opening.
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