A wall-law approximation for Jeffery-Hamel flows in rough wedges

Abstract

We study the two-dimensional stationary Navier-Stokes equations in an unbounded wedge with small rough perturbations of its angular boundaries. The Jeffery-Hamel flow in the corresponding straight wedge is taken as the effective background flow. Under a suitable small-flux condition, we prove the existence of weak solutions and establish an $H^1$-type energy error estimate of order $O({\epsilon }^2)$. For sufficiently small wedge angles, we further derive weighted estimates and improve the squared $L^2$-error to $O({\epsilon }^3)$.

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