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Global-in-time existence results for the two-dimensional Hasegawa-Wakatani equations. (English) Zbl 1423.76492

Summary: In order to describe the resistive drift wave turbulence appearing in nuclear fusion plasma, the Hasegawa-Wakatani (HW) equations were proposed in [A. Hasegawa and M. Wakatani, “Plasma edge turbulence”, Phys. Rev. Lett. 50, No. 9, 682–686 (1983; doi:10.1103/physrevlett.50.682)]. We consider the two-dimensional HW equations, which have numerous structures (that is, they explain the branching phenomenon in turbulent and zonal flow in a two-dimensional plasma) and the generalized HW equations that include temperature fluctuation. We prove the global-in-time existence of a unique strong solution to both the HW equations and the generalized HW equations in a two-dimensional domain with double periodic boundary conditions.

MSC:

76W05 Magnetohydrodynamics and electrohydrodynamics
35K45 Initial value problems for second-order parabolic systems
35Q60 PDEs in connection with optics and electromagnetic theory
82D10 Statistical mechanics of plasmas
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