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Preprints, Working Papers, ... Year : 2017

Stability of stationary viscous incompressible flow around a rigid body performing a translation

Abstract

Suppose a rigid body moves steadily and without rotation in a viscous incompressible fluid, and the flow around the body is steady, too. Such a flow is usually described by the stationary Navier-Stokes system with Oseen term, in an exterior domain. An Oseen term arises because the velocity field is scaled in such a way that it vanishes at infinity. In the work at hand, such a velocity field, denoted by U, is considered as given. We study a solution of the incompressible evolutionary Navier-Stokes system with the same right-hand side and the same Dirichlet boundary conditions as the stationary problem, and with U+u_0 as initial data, where u_0 is a H^1-function. Under the assumption that the H^1-norm of u_0 is small (u_0 a ``perturbation of U'') and that the eigenvalues of a certain linear operator have negative real part, we show that the L^2-norm of the gradient of the difference v(t)-U tends to zero when t tends to infinity (''stability of v''), where v denotes the velocity part of the solution to the initial-boundary value problem under consideration.
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Dates and versions

hal-01534693 , version 1 (08-06-2017)

Identifiers

  • HAL Id : hal-01534693 , version 1

Cite

Paul Deuring. Stability of stationary viscous incompressible flow around a rigid body performing a translation. 2017. ⟨hal-01534693⟩

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