Revista Matemática Iberoamericana


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Volume 31, Issue 1, 2015, pp. 267–290
DOI: 10.4171/RMI/833

Published online: 2015-03-05

On the existence of almost-periodic solutions for the 2D dissipative Euler equations

Luigi C. Berselli[1] and Luca Bisconti[2]

(1) Università di Pisa, Italy
(2) Universita degli Studi di Firenze, Italy

In this paper we study the two-dimensional dissipative Euler equations in a smooth and bounded domain. In the presence of a sufficiently large dissipative term (or equivalently a sufficiently small external force) precise uniform estimates on the modulus of continuity of the vorticity are proved. These allow us to show existence of Stepanov almost-periodic solutions.

Keywords: Euler equations, continuous and Dini-continuous functions, almost-periodic solutions, transport equation

Berselli Luigi, Bisconti Luca: On the existence of almost-periodic solutions for the 2D dissipative Euler equations. Rev. Mat. Iberoam. 31 (2015), 267-290. doi: 10.4171/RMI/833