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12
Diffusion in PoroElastic Media
 Jour. Math. Anal. Appl
, 1998
"... . Existence, uniqueness and regularity theory is developed for a general initialboundaryvalue problem for a system of partial differential equations which describes the Biot consolidation model in poroelasticity as well as a coupled quasistatic problem in thermoelasticity. Additional effects of se ..."
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Cited by 10 (7 self)
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. Existence, uniqueness and regularity theory is developed for a general initialboundaryvalue problem for a system of partial differential equations which describes the Biot consolidation model in poroelasticity as well as a coupled quasistatic problem in thermoelasticity. Additional effects of secondary consolidation and pore fluid exposure on the boundary are included. This quasistatic system is resolved as an application of the theory of linear degenerate evolution equations in Hilbert space, and this leads to a precise description of the dynamics of the system. 1. Introduction We shall consider a system modeling diffusion in an elastic medium in the case for which the inertia effects are negligible. This quasistatic assumption arises naturally in the classical Biot model of consolidation for a linearly elastic and porous solid which is saturated by a slightly compressible viscous fluid. The fluid pressure is denoted by p(x; t) and the displacement of the structure by u(x; t). ...
Mathematical Derivation Of The Power Law Describing Polymer Flow Through A Thin Slab
"... . We consider the polymer flow through a slab of thickness ffl. The flow is described by 3D incompressible NavierStokes system with a nonlinear viscosity, being a power of a norm of the shear rate (power law). We consider the limit when ffl ! 0 and prove that the limit averaged velocity, averaged o ..."
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Cited by 3 (2 self)
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. We consider the polymer flow through a slab of thickness ffl. The flow is described by 3D incompressible NavierStokes system with a nonlinear viscosity, being a power of a norm of the shear rate (power law). We consider the limit when ffl ! 0 and prove that the limit averaged velocity, averaged over the thickness, satisfies a nonlinear twodimensional Poiseuille's law, with nonlinear viscosity depending on the power of the length of the gradient of the pressure. It is found out that the powers in the starting law and in the limit law are conjugate. Furthermore, we prove a convergence theorem for velocity and pressure in appropriate functional spaces. 1 Equipe d'Analyse Numerique, Universit'e de SaintEtienne, 23 rue du Dr. P. Michelon, 42023 SaintEtienne Cedex, France 2 University of Zagreb, Croatia L.A.N., Bat 101, Universit'e Claude Bernard, 43 Bd. du 11 Novembre 1918, F69622 Villeurbanne Cedex, France 2 Andro Mikeli'c and Roland Tapi'ero 1. STATEMENT OF THE PROBLEM AND...
Steady compressible Oseen flow with slip boundary conditions
, 807
"... We prove the existence of solution in a class H 2 (Ω) × H 1 (Ω) to steady compressible Oseen system with slip boundary conditions in a two dimensional, convex domain with the boundary of class H 5/2. The method is to regularize a weak solution obtained via the Galerkin method. The problem of regula ..."
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Cited by 2 (0 self)
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We prove the existence of solution in a class H 2 (Ω) × H 1 (Ω) to steady compressible Oseen system with slip boundary conditions in a two dimensional, convex domain with the boundary of class H 5/2. The method is to regularize a weak solution obtained via the Galerkin method. The problem of regularization is reduced to a problem of solvability of a certain transport equation by application of the Helmholtz decomposition. The method works under additional assumption on the geometry of the boundary.
Steady compressible NavierStokes flow in a square
, 901
"... We investigate a steady flow of compressible fluid with inflow boundary condition on the density and slip boundary conditions on the velocity in a square domain Q ∈ R 2. We show existence if a solution (v, ρ) ∈ W 2 p (Q) × W 1 p (Q) that is a small perturbation of a constant flow (¯v ≡ [1, 0], ¯ρ ..."
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We investigate a steady flow of compressible fluid with inflow boundary condition on the density and slip boundary conditions on the velocity in a square domain Q ∈ R 2. We show existence if a solution (v, ρ) ∈ W 2 p (Q) × W 1 p (Q) that is a small perturbation of a constant flow (¯v ≡ [1, 0], ¯ρ ≡ 1). We also show that this solution is unique in a class of small perturbations of the constant flow (¯v, ¯ρ). In order show the existence of the solution we adapt the techniques know from the theory of weak solutions. We apply the method of elliptic regularization and a fixed point argument. MSC: 35Q30; 76N10 Keywords: NavierStokes equations, steady compressible flow, inflow boundary condition, slip boundary conditions, strong solutions 1 Introduction and main results The problems of steady compressible flows described by the NavierStokes equations are usually considered with the homogeneous Dirichlet boundary conditions on the velocity. It is worth from the mathematical point of view, as well as in the eye of applications, to investigate different
HOMOGENIZATIONLIMIT OF A MODEL SYSTEM FOR INTERACTION OF FLOW, CHEMICAL REACTIONS AND MECHANICS IN CELL TISSUES
"... Abstract. In this article we obtain rigorously the homogenization limit for a fluidstructurereactive flow system. It consists of cell tissue and intercellular liquid, transporting solutes. The cell tissue is supposed linearly elastic and deforming with a viscous nonstationary flow. The elastic mod ..."
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Abstract. In this article we obtain rigorously the homogenization limit for a fluidstructurereactive flow system. It consists of cell tissue and intercellular liquid, transporting solutes. The cell tissue is supposed linearly elastic and deforming with a viscous nonstationary flow. The elastic moduli of the tissue change with cumulative concentration value. In the limit, when the scale parameter goes to zero, we obtain the quasistatic Biot system, coupled with the upscaled reactive flow. Effective Biot’s coefficients depend on the reactant concentration. Additionally to the weak twoscale convergence results, we prove convergence of the elastic and viscous energies. This then implies a strong twoscale convergence result for the fluidstructure variables. Next we establish the regularity of the solutions for the upscaled equations. In our knowledge, it is the only known study of the regularity of solutions to the quasistatic Biot system. The regularity is used to prove the uniqueness for the upscaled model.
EXACT SOLUTION OF MAGNETOHYDRODYNAMIC SYSTEM WITH NON LINEARITY ANALYSIS
"... Analytical and numerical solution of Navier Stokes equation coupled with Maxwell’s equation have been proposed with its experimental prototype model. The MHD system based on two and three dimensional processes were formulated and simulated using MATLAB with iterative approach. Experimental results w ..."
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Analytical and numerical solution of Navier Stokes equation coupled with Maxwell’s equation have been proposed with its experimental prototype model. The MHD system based on two and three dimensional processes were formulated and simulated using MATLAB with iterative approach. Experimental results were obtained by the developed prototype model. Non Linearity issues i.e. turbulence in fluid flow in MHD system were investigated. We have extended the work presented in reference [1], wherein only two dimensional solutions were suggested.
unknown title
, 2009
"... On an inhomogeneous slipinflow boundary value problem for a steady flow of a viscous compressible fluid in a cylindrical domain ..."
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On an inhomogeneous slipinflow boundary value problem for a steady flow of a viscous compressible fluid in a cylindrical domain
Global Wellposedness of the Free Boundary Value Problem of the Incompressible NavierStokes Equations With Surface Tension
"... In this paper, we study the global wellposedness of the NavierStokes equations with free boundary under the surface tension and gravity in three dimensions. For simplicity, we take a moving domain of finite depth, bounded above by free surface and bounded below by a solid flat bottom. We show that ..."
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In this paper, we study the global wellposedness of the NavierStokes equations with free boundary under the surface tension and gravity in three dimensions. For simplicity, we take a moving domain of finite depth, bounded above by free surface and bounded below by a solid flat bottom. We show that there is a unique, globalintime solution provided that the initial velocity and the initial profile of the surface are sufficiently small in Sobolev spaces. The main result of this paper is the continuity of the solution at t = 0, with initial data of lower regularities. In Appendix, we present local wellposedness results to the problem without surface tension. 1.