In this paper, we are concerned with the drift wave turbulence in a strong magnetic field. We prove the existence and uniqueness of a strong global in time solution to the initial boundary value problem for the model equations of drift wave turbulence similar to Hasegawa–Mima equation. Then we prove that the solution of Hasegawa–Wakatani equations established in  converges to that of Hasegawa–Mima like equation established at the first stage as the resistivity tends to zero on some time interval.
Shintaro Kondo. Atusi Tani. "On the Hasegawa–Wakatani equations with vanishing resistivity." Proc. Japan Acad. Ser. A Math. Sci. 87 (9) 156 - 161, November 2011. https://doi.org/10.3792/pjaa.87.156