Almost-periodic solution of linearized Hasegawa–Wakatani equations with vanishing resistivity
Kondo, Shintaro
Rendiconti del Seminario Matematico della Università di Padova, Tome 134 (2015), p. 215-240 / Harvested from Numdam
Publié le : 2015-01-01
@article{RSMUP_2015__133__215_0,
     author = {Kondo, Shintaro},
     title = {Almost-periodic solution of linearized Hasegawa--Wakatani equations with vanishing resistivity},
     journal = {Rendiconti del Seminario Matematico della Universit\`a di Padova},
     volume = {134},
     year = {2015},
     pages = {215-240},
     mrnumber = {3354952},
     language = {en},
     url = {http://dml.mathdoc.fr/item/RSMUP_2015__133__215_0}
}
Kondo, Shintaro. Almost-periodic solution of linearized Hasegawa–Wakatani equations with vanishing resistivity. Rendiconti del Seminario Matematico della Università di Padova, Tome 134 (2015) pp. 215-240. http://gdmltest.u-ga.fr/item/RSMUP_2015__133__215_0/

[1] L. AmerioG. Prouse, Almost-periodic functions and functional equations, Van Nostrand Reinhold Company, New York, 1971. | MR 275061 | Zbl 0215.15701

[2] J. AndresA. M. BersaniR. F. Grande, Hierarchy of almost-periodic function spaces, Rend. Mat. Appl., VII. Ser., 26 (2006), pp. 121–188. | MR 2275292 | Zbl 1133.42002

[3] L. C. BerselliM. Romito, On Leray’s problem for almost periodic flows, J. Math. Sci. Univ. Tokyo, 19 (2012), pp. 69–130. | MR 2977342

[4] A. S. Besicovitch, On generalized almost periodic functions, Proc. L. M. S., 2 (1926), pp. 495–512. | JFM 52.0263.01 | MR 1575297

[5] A. S. Besicovitch, Almost periodic functions, Dover Publ. Inc., New York, 1955. | MR 68029 | Zbl 0065.07102

[6] A. S. BesicovitchH. Bohr, Some remarks on generalisations of almost periodic functions, Meddelelser København, 8 (1927), pp. 1–33. | JFM 53.0240.03

[7] S. Bochner, Abstrakte fastperiodische Funktionen, Acta Math., 61 (1933), pp. 149–184. | JFM 59.0997.01 | MR 1555374

[8] S. Bochner, Fastperiodische Lösungen der Wellengleichung, Acta Math., 62 (1934), pp. 227–237. | JFM 60.0448.01

[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 52.0330.04 | MR 1555216

[10] H. Bohr, Almost periodic functions, Chelsea, New York, 1947. | MR 20163 | Zbl 0278.42019

[11] G. BrunoR. GrandeR. Iannacci, Almost-periodic multipliers, Acta Appl. Math., 65 (2001), pp. 137–151. | MR 1843789 | Zbl 1004.42014

[12] R. Cooke, Almost-periodic functions, Am. Math. Mon., 88 (1981), pp. 515–526. | MR 628019 | Zbl 0473.42011

[13] C. Corduneanu, Almost periodic functions, 2nd Engl. ed., Chelsea, New York, 1989. | Zbl 0672.42008

[14] R. Doss, Contribution to the theory of almost-periodic functions, Ann. Math., 46 (1945), pp. 196–219. | MR 12150 | Zbl 0061.16404

[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. | Numdam | MR 147798 | Zbl 0111.29503

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

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

[18] A. HasegawaK. Mima, Pseudo-three-dimensional turbulence in magnetized nonuniform plasma, Phys. Fluids, 21 (1978), pp. 87–92. | MR 455878 | Zbl 0374.76046

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

[20] A. HasegawaM. Wakatani, A collisional drift wave description of plasma edge turbulence, Phys. Fluids, 27 (1984), pp. 611–618. | Zbl 0579.76052

[21] S. KondoA. Tani, Initial boundary value problem for model equations of resistive drift wave turbulence, SIAM J. Math. Anal., 43 (2011), pp. 925–943. | MR 2801183 | Zbl 1225.35228

[22] S. KondoA. Tani, Initial boundary value problem of Hasegawa–Wakatani equations with vanishing resistivity, Adv. Math. Sci. Appl., 21 (2011), pp. 223–253. | MR 2883882 | Zbl 1235.35268

[23] S. KondoA. Tani, On the Hasegawa–Wakatani equations with vanishing resistivity, Proc. Japan Acad., 87 (2011), pp. 156–161. | MR 2863358 | Zbl 1242.35028

[24] S. KondoA. 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 793735 | Zbl 0588.35003

[26] O. A. LadyzhenskayaV. A. SolonnikovN. N. UralʼCeva, Linear and quasi-linear equations of parabolic type, Amer. Math. Soc., Providence, RI, 1968. | Zbl 0164.12302

[27] G. T. LavarnwayR. Cooke, A characterization of Fourier series of Stepanov almost-periodic functions, J. Fourier Anal. Appl., 7 (2001), pp. 127–142. | MR 1817672 | Zbl 0985.42005

[28] P. MarcatiA. Valli, Almost-periodic solutions to the Navier-Stokes equations for compressible fluids, Boll. Un. Mat. Ital., VI. Ser., B4 (1985), pp. 969–986. | MR 831301 | Zbl 0633.76067

[29] V. S. MikhailenkoV. V. MikhailenkoK. N. StepanovN. 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 232070

[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. | Numdam | MR 167736 | Zbl 0117.07303

[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 1031744 | Zbl 0696.35128

[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 211083 | Zbl 0164.12502

[34] V. V. Stepanov, Sur quelques généralisations des fonctions presque périodiques, C. R. Acad. Sci. Paris, 181 (1925), pp. 90–92. | JFM 51.0214.01

[35] V. V. Stepanov, Über einige Verallgemeinerungen der fastperiodischen Funktionen, Math. Ann., 95 (1926), pp. 473–498. | JFM 52.0262.01 | MR 1512290

[36] J. Wesson, Tokamaks, Oxford Univ. Press, New York, 1987. | Zbl 1111.82054

[37] N. Wiener, On the representation of functions by trigonometrical integrals, Math. Zeitschr., 24 (1925), pp. 575–616. | JFM 51.0228.06

[38] S. Zaidman, Almost-periodic functions in abstract spaces, Res. Notes in Math., 126, Pitman, Boston, 1985. | MR 790316 | Zbl 0648.42006