Spontaneous periodic orbits in the Navier-Stokes flow via computer-assisted proofs

28 January 2021
Jean-Philippe Lessard
In this talk, we introduce a general method to obtain constructive proofs of existence of periodic orbits in the forced autonomous Navier-Stokes equations on the three-torus. After introducing a zero finding problem posed on a Banach space of geometrically decaying Fourier coefficients, a Newton-Kantorovich theorem is applied to obtain the (computer-assisted) proofs of existence. As applications, we present proofs of existence of spontaneous periodic orbits in the Navier-Stokes equations with Taylor-Green forcing.


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  • Computational Mathematics and Applications Seminar