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

Kondo, Shintaro; Tani, Atusi

Proc. Japan Acad., Ser. A 87, No. 9, 156-161 (2011).

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.

Reviewer: Alexander Mikhajlovich Blokhin (Novosibirsk)

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

References:

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