## On the Hasegawa-Wakatani equations with vanishing resistivity.(English)Zbl 1242.35028

The paper is devoted to proving the convergence as $$\varepsilon \rightarrow 0$$ of solutions to the Hasegawa-Wakatani equations $$(\Phi^{\varepsilon}, n^{\varepsilon})$$ to the solution $$(\Phi^{0}, n^{0})$$ to the limit Hasegawa-Wakatani equation where formally $$\varepsilon=0$$; the parameter $$\varepsilon$$ is linearly dependent on the resistivity $$\eta$$. It is shown that the convergence in Sobolev spaces takes place on a time interval $$[0,T]$$ where the constant $$T$$ is finally determined via the initial data $$(\Phi_0^{0}, n_0^{0})$$, what in principal means the time locality of the described result. In this connection a question arises: what happens when $$t>T$$? The answer to this question could be obtained for example after an adequate numerical experiment.

### MSC:

 35B25 Singular perturbations in context of PDEs 35K45 Initial value problems for second-order parabolic systems 35Q60 PDEs in connection with optics and electromagnetic theory 82D10 Statistical mechanics of plasmas 35B40 Asymptotic behavior of solutions to PDEs

### Keywords:

Hasegawa-Mima equation; drift wave turbulence
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### References:

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