Revista Matemática Iberoamericana
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Published online: 2015-03-05
On the existence of almost-periodic solutions for the 2D dissipative Euler equationsLuigi C. Berselli and Luca Bisconti (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