1,721,230 research outputs found

    A representation formula for the steady solutions of a compressible fluid moving at low speed

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    We prove existence and a representation formula for solutions to the equations describing steady flows of an isothermal, viscous, compressible gas having a positive infimum for the density p, moving at low speed, under the action of sufficiently small external forces. If the infimum of p is zero, then conditions are furnished under which only the trivial vacuum solution exists. © 1992, Taylor & Francis Group, LLC. All rights reserved

    Existence and asymptotic behaviour of steady flow of a viscous barotropic gas in a pipe

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    Existence and asymptotic behaviour of steady flow of a viscous barotropic gas in a pipe is analyzed

    In a horizontal layer with free upper surface

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    On existence of non steady compressible viscous flows in a horizontal layer with free upper surface, in a small time interval. The proof adapt a Galerkin procedure

    Stability and decay to zero of the L^2 norms of perturbations to a viscous compressible heat conductive fluid motion exterior to a ball

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    Stability and decay to zero of the L^2 norms of perturbations to a viscous compressible heat conductive fluid motion exterior to a ball, under suitable summability in space condition on the perturbation to the density

    Steady flows of compressible fluids in a rigid container with upper free boundary

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    We consider fluid in a smooth rigid container whose lateral boundary is a piece of vertical cylinder, bounded above by a free upper surface. As basic flow we consider the non homogeneous rest state in the presence of gravity, and of a surface tension. Under these assumptions, we study the existence of a steady free boundary Gamma and a steady motion in Omega of an isothermal viscous gas, resulting as perturbation to the rest state in correspondence of small non potential perturbations to the (large potential) gravitational force. We linearize the problem by prescribing the unknown domain Omega, then we make use of the iterative scheme introduced by Heywood and Padula. Our method is based on an iteration between the Neumann problem for a non homogeneous Stokes system for the velocity, the Neumann problem for an elliptic problem on Gamma for height, and a steady transport equation for the perturbation to the density. The difference of boundary condition between lateral boundary and free upper surfaces causes a singularity at the intersection (contact line). To avoid singularities on the contact line, we adopt weighted Sobolev spaces

    Free Work and Control of Equilibrium Configurations

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    Physical and geometrical discussion on interface is developed. Mathematical position of the problem is clarified. Results achievedare described. Outline of uniqueness proof is shown
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