# Rendiconti del Seminario Matematico della Università di Padova

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**Volume 133, 2015, pp. 215–239**

**DOI: 10.4171/RSMUP/133-11**

Almost-periodic solution of linearized Hasegawa–Wakatani equations with vanishing resistivity

Shintaro Kondo^{[1]}(1) Meiji Institute for Advanced Study of Math Sciences, Meiji University, 4-21-1 Nakano Nakano-ku, 164-8525, Tokyo, Japan

In this paper we consider the zero-resistivity limit for linearized Hasegawa–Wakatani equations in a cylindrical domain when the initial data are Stepanov-almost-periodic to the axial direction. We prove two results: one is the existence and uniqueness of a strong Stepanov-almost-periodic solution to the initial boundary value problem for linearized Hasegawa–Wakatani equations with zero resistivity; another is the convergence of the solution of linearized Hasegawa–Wakatani equations established in [24] to the solution of the problem studied at the first stage as the resistivity tends to zero. In the proof we obtain two useful lemmas for Stepanov-almost-periodic functions.

*Keywords: *Hasegawa–Wakatani equations, Hasegawa–Mima equation, drift wave turbulence, Sobolev spaces, Stepanov-almost-periodic function

Kondo Shintaro: Almost-periodic solution of linearized Hasegawa–Wakatani equations with vanishing resistivity . *Rend. Sem. Mat. Univ. Padova* 133 (2015), 215-239. doi: 10.4171/RSMUP/133-11