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We prove the existence of steady \emph{space quasi-periodic} streamfunctions, solutions for the Euler equation in vorticity-stream functionformulation in the two dimensional channel ${\mathbb R}\times [-1,1]$. Thesesolutions bifurcate from a prescribed shear equilibrium near the Couette flow,whose profile induces finitely many modes of oscillations in the horizontaldirection for the linearized problem. Using a Nash-Moser implicit functioniterative scheme, near such equilibrium we construct small amplitude, spacereversible stream functions slightly deforming the linear solutions andretaining the horizontal quasi-periodic structure. These solutions exist formost values of the parameters characterizing the shear equilibrium. As aby-product, the streamlines of the nonlinear flow exhibit Kelvin's cat eye-liketrajectories arising from the finitely many stagnation lines of the shearequilibrium.

Space quasi-periodic steady Euler flows close to the inviscid Couette flow