| Abstract: |
| Invariant structures and asymptotic behaviours close to shear flows are of great interest in Fluid Dynamics. In this short talk, I present a recent result about the existence of nontrivial steady flows in the bounded 2D channel that are quasi-periodic in the horizontal space direction and solve the incompressible Euler equation. In particular, we work with steady Euler flows that solve some semilinear elliptic equations in the space domain, where we are led to use the horizontal direction as a time coordinate.
Such solutions bifurcate from a prescribed shear equilibrium near the Couette flow, whose profile induces finitely many modes of oscillations in the horizontal direction that may be resonant. This leads to a small divisor problem and the consequent loss of derivatives is overcome with a Nash-Moser nonlinear iteration.
This is a joint work with Nader Masmoudi and Riccardo Montalto |
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