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In order to describe the resistive drift wave turbulence appearing in nuclear fusion plasma, the Hasegawa–Wakatani equations were proposed in 1983. In this paper, we consider the zero-resistivity limit for the Hasegawa–Wakatani equations in a cylindrical domain when the initial data are Stepanov-almost-periodic in the axial direction. We prove two results: one is the existence and uniqueness of a strong global in time Stepanov-almost-periodic solution to the initial boundary value problem for the Hasegawa–Mima-like equation; another is the convergence of the solution of the Hasegawa–Wakatani equations to that of the Hasegawa–Mima-like equation established at the first stage as the resistivity tends to zero. In order to obtain a priori estimates of the Stepanov-almost-periodic solutions to our problems, we have to overcome some difficulties. In the proof, we prepare some lemmas for the Stepanov-almost-periodic functions and then obtain a priori estimates.
Journal of Evolution Equations – Springer Journals
Published: Mar 1, 2016
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