Rendiconti del Seminario Matematico della Università di Padova
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Almost-periodic solution of linearized Hasegawa–Wakatani equations with vanishing resistivityShintaro Kondo (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  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