. Existence, uniqueness and regularity theory is developed for a general initial-boundary-value 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 quasi-static 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 quasi-static 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). ...

. We consider the polymer flow through a slab of thickness ffl. The flow is described by 3D incompressible Navier-Stokes 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 two-dimensional Poiseuille's law, with non-linear 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 Saint-Etienne, 23 rue du Dr. P. Michelon, 42023 Saint-Etienne 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...

residual methods for solving steady fluid flows

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: Navier-Stokes 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 Navier-Stokes 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

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.