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An almost-periodic solution of Hasegawa–Wakatani equations with vanishing resistivity

Part of: Applications to specific types of physical systems Harmonic analysis in one variable Parabolic equations and systems Equations of mathematical physics and other areas of application Harmonic analysis in several variables

Published online by Cambridge University Press:  23 June 2016

Shintaro Kondo
Shintaro Kondo*
Affiliation:
Meiji Institute for Advanced Study of Mathematical Sciences, Meiji University, 4-21-1 Nakano, Nakano-ku, Tokyo 164-8525, Japan ([email protected])
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Extract

We consider the zero-resistivity limit for Hasegawa–Wakatani equations in a cylindrical domain when the initial data are Stepanov almost-periodic in the axial direction. First, we prove the existence of a solution to Hasegawa–Wakatani equations with zero resistivity; second, we obtain uniform a priori estimates with respect to resistivity. Such estimates can be obtained in the same way as for our previous results; therefore, the most important contribution of this paper is the proof of the existence of a local-in-time solution to Hasegawa–Wakatani equations with zero resistivity. We apply the theory of Bohr–Fourier series of Stepanov almost-periodic functions to such a proof.

Keywords

Hasegawa–Wakatani equationsdrift wave turbulencealmost-periodic function

MSC classification

Secondary: 35Q60: PDEs in connection with optics and electromagnetic theory 35K45: Initial value problems for second-order parabolic systems 42A75: Classical almost periodic functions, mean periodic functions 42B05: Fourier series and coefficients 82D10: Plasmas
Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 146 , Issue 5 , October 2016 , pp. 983 - 1003
Copyright
Copyright © Royal Society of Edinburgh 2016 

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