Hiroko Morimoto

CHAPTER 5 – Stationary Navier–Stokes Flow in 2-D Channels Involving the General Outflow Condition

Abstract Let Ω be a two-dimensional multiply connected domain with unbounded smooth boundary. We suppose that Ω has several outlets. The boundary ∂Ω has, besides the inÞnite part Γ 0 , several bounded connected components, Γ 1 , Γ 2 ,…, Γ N . We study the existence of the stationary NavierĐStokes sow in Ω satisfying prescribed non-zero sux on every Γ i (1 ⩽ i ⩽ N ) and tending to the prescribed Poiseuille sow at the inÞnity. Assume that the domain and the boundary value are symmetric with respect to the x 1 -axis and every Γ i (1 ⩽ i ⩽ N ) intersects the x 1 -axis. Then, we can show the existence of weak solution for small Poiseuille sows and arbitrary large boundary value. The regularity of the solution and the asymptotic behavior at the inÞnity are also discussed.

On stationary Navier-Stokes flows in 2D semi-infinite channel involving the general outflow condition

SuntoIn questo lavoro consideriamo le equazioni di Navier-Stokes stazionarie in un certo tipo di canali semi-infiniti sotto la condizione generale di outflow. Assumendo che sia il dominio sia i dati siano simmetrici rispetto ad una retta, l’asse di simmetria, e che questa retta intersechi ogni componente del bordo, mostriamo esistenza di soluzioni ed alcune proprietà di regolarità delle stesse.SummaryWe consider the stationary Navier-Stokes equations in a certain type of semi-infinite channel under the general outflow condition. Assuming that the domain and the data are symmetric with respect to a straight line, the axis of symmetry, and that the axis intersects every component of the boundary, we show the existence of solutions and certain regularity properties of the solutions.