Spontaneous periodic orbits in the Navier-Stokes flow

Autor:	Berg, Jan Bouwe van den, Breden, Maxime, Lessard, Jean-Philippe, van Veen, Lennaert
Rok vydání:	2019
Předmět:	Mathematics - Analysis of PDEs Physics - Fluid Dynamics 35Q30 35B06 35B10 35B36 65G20 76D17
Druh dokumentu:	Working Paper
Popis:	In this paper, a general method to obtain constructive proofs of existence of periodic orbits in the forced autonomous Navier-Stokes equations on the three-torus is proposed. 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. The required analytic estimates to verify the contractibility of the operator are presented in full generality and symmetries from the model are used to reduce the size of the problem to be solved. As applications, we present proofs of existence of spontaneous periodic orbits in the Navier-Stokes equations with Taylor-Green forcing. Comment: 52 pages, 4 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1902.00384 Zobrazit plný text záznamu View this record from Arxiv