Almost-periodic solution of linearized Hasegawa–Wakatani equations with vanishing resistivity
Rendiconti del Seminario Matematico della Università di Padova, Tome 133 (2015), pp. 215-240. 
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     author = {Kondo, Shintaro},
     title = {Almost-periodic solution of linearized {Hasegawa{\textendash}Wakatani} equations with vanishing resistivity},
     journal = {Rendiconti del Seminario Matematico della Universit\`a di Padova},
     pages = {215--240},
     publisher = {Seminario Matematico of the University of Padua},
     volume = {133},
     year = {2015},
     mrnumber = {3354952},
     language = {en},
     url = {http://www.numdam.org/item/RSMUP_2015__133__215_0/}
}
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Kondo, Shintaro. Almost-periodic solution of linearized Hasegawa–Wakatani equations with vanishing resistivity. Rendiconti del Seminario Matematico della Università di Padova, Tome 133 (2015), pp. 215-240. http://www.numdam.org/item/RSMUP_2015__133__215_0/

[1] L. Amerio – G. Prouse, Almost-periodic functions and functional equations, Van Nostrand Reinhold Company, New York, 1971. | MR | Zbl

[2] J. Andres – A. M. Bersani – R. F. Grande, Hierarchy of almost-periodic function spaces, Rend. Mat. Appl., VII. Ser., 26 (2006), pp. 121–188. | MR | Zbl

[3] L. C. Berselli – M. Romito, On Leray’s problem for almost periodic flows, J. Math. Sci. Univ. Tokyo, 19 (2012), pp. 69–130. | MR

[4] A. S. Besicovitch, On generalized almost periodic functions, Proc. L. M. S., 2 (1926), pp. 495–512. | JFM | MR

[5] A. S. Besicovitch, Almost periodic functions, Dover Publ. Inc., New York, 1955. | MR | Zbl

[6] A. S. Besicovitch – H. Bohr, Some remarks on generalisations of almost periodic functions, Meddelelser København, 8 (1927), pp. 1–33. | JFM

[7] S. Bochner, Abstrakte fastperiodische Funktionen, Acta Math., 61 (1933), pp. 149–184. | JFM | MR

[8] S. Bochner, Fastperiodische Lösungen der Wellengleichung, Acta Math., 62 (1934), pp. 227–237. | JFM

[9] H. Bohr, Zur Theorie der fastperiodischen Funktionen. I, Acta Math., 45 (1924), pp. 29–127; II, Ibid., 46 (1925), pp. 101–214; III, Ibid., 47 (1926), pp. 237–281. | JFM | MR

[10] H. Bohr, Almost periodic functions, Chelsea, New York, 1947. | MR | Zbl

[11] G. Bruno – R. Grande – R. Iannacci, Almost-periodic multipliers, Acta Appl. Math., 65 (2001), pp. 137–151. | MR | Zbl

[12] R. Cooke, Almost-periodic functions, Am. Math. Mon., 88 (1981), pp. 515–526. | MR | Zbl

[13] C. Corduneanu, Almost periodic functions, 2nd Engl. ed., Chelsea, New York, 1989. | Zbl

[14] R. Doss, Contribution to the theory of almost-periodic functions, Ann. Math., 46 (1945), pp. 196–219. | MR | Zbl

[15] C. Foias, Essais dans l’étude des solutions des équations de Navier–Stokes dans l’espace. L’unicité et la presque-périodicité des solutions petites, Rend. Sem. Mat. Univ. Padova, 32 (1962), pp. 261–294. | EuDML | Numdam | MR | Zbl

[16] Ö. D. Gürcan – P. H. Diamond – T. S. Hahm, Radial transport of fluctuation energy in a two-field model of drift-wave turbulence, Phys. Plasmas, 13 (2006), article 052306.

[17] A. Hasegawa – K. Mima, Stationary spectrum of strong turbulence in magnetized plasma, Phys. Rev. Lett., 39 (1977), pp. 205–208.

[18] A. Hasegawa – K. Mima, Pseudo-three-dimensional turbulence in magnetized nonuniform plasma, Phys. Fluids, 21 (1978), pp. 87–92. | MR | Zbl

[19] A. Hasegawa – M. Wakatani, Plasma edge turbulence, Phys. Rev. Lett., 50 (1983), pp. 682–686.

[20] A. Hasegawa – M. Wakatani, A collisional drift wave description of plasma edge turbulence, Phys. Fluids, 27 (1984), pp. 611–618. | Zbl

[21] S. Kondo – A. Tani, Initial boundary value problem for model equations of resistive drift wave turbulence, SIAM J. Math. Anal., 43 (2011), pp. 925–943. | MR | Zbl

[22] S. Kondo – A. Tani, Initial boundary value problem of Hasegawa–Wakatani equations with vanishing resistivity, Adv. Math. Sci. Appl., 21 (2011), pp. 223–253. | MR | Zbl

[23] S. Kondo – A. Tani, On the Hasegawa–Wakatani equations with vanishing resistivity, Proc. Japan Acad., 87 (2011), pp. 156–161. | MR | Zbl

[24] S. Kondo – A. Tani, Almost-periodic solutions to initial boundary value problem for model equations of resistive drift wave turbulence, Ann. Scuola Norm. Sup. Pisa, to appear.

[25] O. A. Ladyzhenskaya, The boundary value problems of mathematical physics, Springer-Verlag, New York, 1985. | MR | Zbl

[26] O. A. Ladyzhenskaya – V. A. Solonnikov – N. N. UralʼCeva, Linear and quasi-linear equations of parabolic type, Amer. Math. Soc., Providence, RI, 1968. | Zbl

[27] G. T. Lavarnway – R. Cooke, A characterization of Fourier series of Stepanov almost-periodic functions, J. Fourier Anal. Appl., 7 (2001), pp. 127–142. | EuDML | MR | Zbl

[28] P. Marcati – A. Valli, Almost-periodic solutions to the Navier-Stokes equations for compressible fluids, Boll. Un. Mat. Ital., VI. Ser., B4 (1985), pp. 969–986. | MR | Zbl

[29] V. S. Mikhailenko – V. V. Mikhailenko – K. N. Stepanov – N. A. Azarenkov, Renormalized non-modal theory of turbulence of plasma shear flows, Plasma Phys., 17 (2011), pp. 41–43.

[30] S. Mizohata, Partial differential equations, Iwanami, Tokyo 1965. (in Japanese) | MR

[31] G. Prouse, Soluzioni quasi-periodiche dell’equazione differenziale di Navier–Stokes in due dimensioni, Rend. Sem. Mat. Univ. Padova, 33 (1963), pp. 186–212. | EuDML | Numdam | MR | Zbl

[32] G. Prouse, Almost-periodic solutions of Navier–Stokes equations and inequalities, Math.-Fys. Medd., K. Dan. Vidensk. Selsk., 42 (1989), pp. 119–123. | MR | Zbl

[33] V. A. Solonnikov, On boundary value problems for linear parabolic systems of differential equations of general form, Trudy Math. Inst. Steklov, 83 (1965), pp. 3–163; English translation: Proc. Steklov Inst. Math., 83 (1965), pp. 1–184. | MR | Zbl

[34] V. V. Stepanov, Sur quelques généralisations des fonctions presque périodiques, C. R. Acad. Sci. Paris, 181 (1925), pp. 90–92. | JFM

[35] V. V. Stepanov, Über einige Verallgemeinerungen der fastperiodischen Funktionen, Math. Ann., 95 (1926), pp. 473–498. | EuDML | JFM | MR

[36] J. Wesson, Tokamaks, Oxford Univ. Press, New York, 1987. | Zbl

[37] N. Wiener, On the representation of functions by trigonometrical integrals, Math. Zeitschr., 24 (1925), pp. 575–616. | EuDML | JFM

[38] S. Zaidman, Almost-periodic functions in abstract spaces, Res. Notes in Math., 126, Pitman, Boston, 1985. | MR | Zbl