We prove the existence of time-quasi-periodic solutions of the incompressible Euler equation on the three-dimensional torus T3, with a small time-quasi-periodic external force. The solutions are perturbations of constant (Diophantine) vector fields, and they are constructed by means of normal forms and KAM techniques for reversible quasilinear PDEs.

Quasi-periodic incompressible Euler flows in 3D / P. Baldi, R. Montalto. - In: ADVANCES IN MATHEMATICS. - ISSN 0001-8708. - 384(2021), pp. 107730.1-107730.74. [10.1016/j.aim.2021.107730]

Quasi-periodic incompressible Euler flows in 3D

R. Montalto
2021

Abstract

We prove the existence of time-quasi-periodic solutions of the incompressible Euler equation on the three-dimensional torus T3, with a small time-quasi-periodic external force. The solutions are perturbations of constant (Diophantine) vector fields, and they are constructed by means of normal forms and KAM techniques for reversible quasilinear PDEs.
Euler equation; Fluid dynamics; KAM for PDEs; Quasi-periodic solutions; Vorticity formulation
Settore MAT/07 - Fisica Matematica
Settore MAT/05 - Analisi Matematica
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/2434/859758
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