Discrete and Continuous Models and Applied Computational ScienceDiscrete and Continuous Models and Applied Computational Science2658-46702658-7149Peoples' Friendship University of Russia8244Research ArticleNVESTIGATION OF THE STABILITY OF THE POTENTIAL FLUID FLOW IN A POROUS MEDIUM WITH VARIABLE TRANSVERSE DIFFUSION COEFFICIENTRybakovYu PDepartment of Theoretical Physics and Mechanicssoliton4@mail.ruSviridovaO DDepartment of Theoretical Physics and Mechanicsoksanasviridova@yandex.ruShikinG NDepartment of Theoretical Physics and Mechanics-Peoples’ Friendship University of Russia15032014318218508092016Copyright © 2014,2014We have considered the potential fluid flow in porous medium taking into account variable diffusion coefficient in the tube of radius . The flow is supposed to be cylindrically-symmetric. The velocity has two components: ⃗ =(,0,). The Euler equation has in the right hand side the term which determines Darcy force: ⃗ = −⃗, where - inverse Darcy coefficient. Continuity equation has the term which describes transverse diffusion of flowing fluid. We have established that for Euler equations system the equality 2/ ≡ 2/ is fulfilled identically. It means that Euler equations system is compatible and integrable. For (,) we have obtained Bessel equation, for (,) - the equation with diffusion coefficient (). We have investigated the solution of the equation for (,) with three types of diffusion coefficient (). We have established that in all cases the equation has unstable solution.potential flowporous mediumDarcy lawstabilitydiffusionпотенциальное течениепористая средазакон Дарсиустойчивостьдиффузия