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Quasi-periodic incompressible Euler flows in 3D. (English) Zbl 1483.37091

Summary: We prove the existence of time-quasi-periodic solutions of the incompressible Euler equation on the three-dimensional torus \(\mathbb{T}^3\), 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.

MSC:

37K55 Perturbations, KAM theory for infinite-dimensional Hamiltonian and Lagrangian systems
35Q31 Euler equations
35Q35 PDEs in connection with fluid mechanics
76B03 Existence, uniqueness, and regularity theory for incompressible inviscid fluids
76D03 Existence, uniqueness, and regularity theory for incompressible viscous fluids
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