Quasi-periodic incompressible Euler flows in 3D

2020/03/31 by Baldi, Pietro, Montalto, Riccardo · 5 citations
#35Q31 #37K55 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2003.14313

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.

Cited by

• Long time dynamics of space periodic water waves
• Symmetries and Weighted Integrability of Vector Fields with Jacobi Multipliers
• Long-wave instability of periodic shear flows for the 2D Navier-Stokes equations
• Linearly Stable KAM Tori for One Dimensional Forced Kirchhoff Equations under Periodic Boundary Conditions
• On the reducibility of the 1d quantum harmonic oscillator with a quasi-periodic bounded potential

Related

• The Navier-Stokes equation with time quasi-periodic external force:\n existence and stability of quasi-periodic solutions
• Time almost-periodic solutions of the incompressible Euler equations
• Quasi-periodic solutions to the incompressible Euler equations in dimensions two and higher
• Dissipative continuous Euler flows in two and three dimensions
• Periodic orbits of Euler vector fields on 3-manifolds