Data di Pubblicazione:
2024
Citazione:
Space Quasi-Periodic Steady Euler Flows Close to the Inviscid Couette Flow / L. Franzoi, N. Masmoudi, R. Montalto. - In: ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS. - ISSN 0003-9527. - 248:(2024), pp. 81.1-81.79. [10.1007/s00205-024-02028-1]
Abstract:
We prove the existence of steady space quasi-periodic stream functions, solutions for the Euler equation in a vorticity-stream function formulation in the two dimensional channel R×[-1,1]. These solutions bifurcate from a prescribed shear equilibrium near the Couette flow, whose profile induces finitely many modes of oscillations in the horizontal direction for the linearized problem. Using a Nash–Moser implicit function iterative scheme, near such equilibrium we construct small amplitude, space reversible stream functions, slightly deforming the linear solutions and retaining the horizontal quasi-periodic structure. These solutions exist for most values of the parameters characterizing the shear equilibrium. As a by-product, the streamlines of the nonlinear flow exhibit Kelvin’s cat eye-like trajectories arising from the finitely many stagnation lines of the shear equilibrium.
Tipologia IRIS:
01 - Articolo su periodico
Keywords:
35Q31; 37K55; 76B03
Elenco autori:
L. Franzoi, N. Masmoudi, R. Montalto
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