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

### Shintaro Kondo

Meiji University, Tokyo, Japan

## Abstract

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.

## Cite this article

Shintaro Kondo, Almost-periodic solution of linearized Hasegawa–Wakatani equations with vanishing resistivity . Rend. Sem. Mat. Univ. Padova 133 (2015), pp. 215–239

DOI 10.4171/RSMUP/133-11