Two Dimensional Incompressible Ideal Flow Around a Small Curve

Two Dimensional Incompressible Ideal Flow Around a Small Curve

Two dimensional incompressible ideal flow around a small obstacle

In this article we study the asymptotic behavior of incompressible, ideal, timedependent two dimensional flow in the exterior of a single smooth obstacle when the size of the obstacle becomes very small. Our main purpose is to identify the equation satisfied by the limit flow. We will see that the asymptotic behavior depends on γ, the circulation around the obstacle. For smooth flow around a si...

Two Dimensional Incompressible Ideal Flow around a Thin Obstacle Tending to a Curve

The purpose of this work is to study the influence of a thin material obstacle on the behavior of two-dimensional incompressible ideal flows. More precisely, we consider a family of obstacles Ωε which are smooth, bounded, open, connected, simply connected subsets of the plane, contracting to a smooth curve Γ as ε → 0. Given the geometry of the exterior domain R \Ωε, a velocity field (divergence...

Two-dimensional Incompressible Viscous Flow around a Small Obstacle

In this work we study the asymptotic behavior of viscous incompressible 2D flow in the exterior of a small material obstacle. We fix the initial vorticity ω0 and the circulation γ of the initial flow around the obstacle. We prove that, if γ is sufficiently small, the limit flow satisfies the full-plane Navier-Stokes system, with initial vorticity ω0 + γδ, where δ is the standard Dirac measure. ...

Two Dimensional Incompressible Viscous Flow Around a Thin Obstacle Tending to a Curve

In [9] the author considered the two dimensional Euler equations in the exterior of a thin obstacle shrinking to a curve and determined the limit velocity. In the present work, we consider the same problem in the viscous case, proving convergence to a solution of the Navier-Stokes equations in the exterior of a curve. The uniqueness of the limit solution is also shown.