Reika Fukuizumi | Publications

Research papers

(maternity leaves in 2013 and 2016)
  1. Anne de Bouard, Arnaud Debussche, and Reika Fukuizumi, "Two dimensional Gross-Pitaevskii equation with space-time white noise,'' Preprint. PDF file
  2. Riccardo Adami, Reika Fukuizumi, and Justin Holmer, "Scattering for the L^2 supercritical point NLS,''to appear in Trans. A.M.S. PDF file
  3. Riccardo Adami, Reika Fukuizumi and Etsuo Segawa, "A nonlinear quantum walk induced by a quantum graph with nonlinear delta potential,'' Quantum Information Processing 18(2019) 119(1)-119(14). PDF file
  4. Anne de Bouard, Arnaud Debussche, and Reika Fukuizumi, "Long time behavior of Gross-Pitaevskii equation at positive temperature,'' SIAM. J. Math. Anal. 50 (2018), 5887-5920. PDF file
  5. Anne de Bouard, Arnaud Debussche, Reika Fukuizumi, and Romain Poncet, ``Fluctuations and temperature effects in Bose-Einstein condensation,'' ESAIM: proceedings and surveys. 61 (2018), 55-67. PDF file
  6. Reika Fukuizumi, Fouad Hadj Selem and Hiroaki Kikuchi, "Corrigendum;Stationary problem related to nonlinear Schrodinger equations on the unit ball,''Nonlinearity. 28 (2015) C3-C7 PDF file
  7. Anne de Bouard, Reika Fukuizumi and Romain Poncet, "Vortex solutions in Bose-Einstein condensation under a trapping potential varying randomly in time,'' Discrete Contin. Dyn. Syst. Ser. B 20 (2015), no. 9, 2793–2817 PDF file
  8. Reika Fukuizumi and Andrea Sacchetti, "Stationary states for nonlinear Schrodinger equations with periodic potentials,'' J. Stat. Phys. 156 (2014) 707-738 PDF file
  9. Anne de Bouard and Reika Fukuizumi, "Representation formula for stochastic Schrodinger evolution equations and applications,'' Nonlinearity 25 (2012) 2993-3022 PDF file
  10. Reika Fukuizumi, Fouad Hadj Selem and Hiroaki Kikuchi, "Stationary problem related to nonlinear Schrodinger equations on the unit ball,'' Nonlinearity 25 (2012) 2271-2301 PDF file
  11. Reika Fukuizumi and Andrea Sacchetti, "Bifurcation and stability for nonlinear Schrodinger equations with double well potential in the semiclassical limit,'' J. Stat. Phys. 145 (2011) 1546-1594 PDF file
  12. Anne de Bouard and Reika Fukuizumi, ''Modulation analysis for a stochastic NLS arising in Bose-Einstein condensation,'' Asymptot. Anal. 63 (2009) 189-235 PDF file
  13. Stefan Le Coz, Reika Fukuizumi, Gadi Fibich, Baruch Ksherim and Yonatan Sivan, ''Instability of bound states of a nonlinear Schrödinger equation with a Dirac potential,'' Physica D. Vol. 237 (2008) pp. 1103--1128 PDF file
  14. Reika Fukuizumi, Masahito Ohta and Tohru Ozawa, ''Nonlinear Schrödinger equation with a point defect,'' Ann. I. H. Poincaré (C)- AN. Vol. 25 (2008) pp. 837--845 PDF file
  15. Reika Fukuizumi and Louis Jeanjean, ''Stability of standing waves for a nonlinear Schrödinger equation with a repulsive Dirac delta potential,'' Discrete Contin. Dynam. Systems. Vol. 21 (2008) pp. 121--136 PDF file
  16. Anne de Bouard and Reika Fukuizumi, ''Stochastic fluctuations in the Gross-Pitaevskii equation,'' Nonlinearity. Vol. 20 (2007) pp. 2823--2844 PDF file
  17. Reika Fukuizumi and Tohru Ozawa, "On a decay property of solutions to the Haraux-Weissler equation", Journal of Differential Equations. Vol. 221 No.1 (2006) pp. 134--142 PDF file
  18. Anne de Bouard and Reika Fukuizumi, "Stability of standing waves for nonlinear Schrödinger equations with inhomogeneous nonlinearities", Annales de l'IHP Vol. 6 (2005) pp. 1--21 PDF file
  19. Reika Fukuizumi and Masahito Ohta, "Instability of standing waves for nonlinear Schrödinger equations with inhomogeneous nonlinearities", Journal of Mathematics of Kyoto University. Vol. 45 No.1 (2005) pp. 145--158
  20. Reika Fukuizumi, "Stability of standing waves for nonlinear Schrödinger equations with critical power nonlinearity and potentials," Advances in Differential Equations. Vol. 10 No. 2 (2005) pp. 259--276
  21. Reika Fukuizumi and Tohru Ozawa, "Exponential decay of solutions to nonlinear elliptic equations with potentials", Z. Angew. Math. Phys. Vol. 56 No. 6 (2005) pp. 1000--1011 PDF file
  22. Reika Fukuizumi, "Remarks on the stable standing waves for nonlinear Schrödinger equations with double power nonlinearity", Advances in Mathematical Sciences and Applications. Vol. 13 No. 2 (2003) pp. 549--564
  23. Reika Fukuizumi and Masahito Ohta, "Stability of standing waves for nonlinear Schrödinger equations with potentials", Differential and Integral Equations. Vol.16 No.1 (2003) pp. 111--128
  24. Reika Fukuizumi and Masahito Ohta, "Instability of standing waves for nonlinear Schrödinger equations with potentials", Differential and Integral Equations. vol.16 No.6 (2003) pp. 691--706
  25. Reika Fukuizumi, "Stability and instability of standing waves for the nonlinear Schrödinger equation with harmonic potential", Discrete Contin. Dynam. Systems. Vol.7 No.3 (2001) pp. 525--544 PDF file

Proceedings

  • "Stability and instability of standing waves for nonlinear Schrödinger equations with harmonic potential," Nonlinear evolution equations and applications, Surikaisekikenkyusho Kokyuroku (Japanese), No. 1197 (2001) 196--206
  • "Stability of standing waves for nonlinear Schrödinger equations with double power nonlinearity" Nonlinear evolution equations and applications, Surikaisekikenkyusho Kokyuroku (Japanese), No. 1388 (2004) 23--33
  • "Stability of standing waves for nonlinear Schrödinger equations with potentials," Séminaire 2003-2004 Équations aux dérivées partielles, Ecole Polytechnique exposé numéro IX
  • "Stability of standing waves for nonlinear Schrödinger equations," Boundary value problem of partial differential equations, Surikaisekikenkyusho Kokyuroku (Japanese), No. 1558 (2007) 65--74.
  • "Gross-Pitaevskii equation under a random external force," Surikaisekikenkyusho Kokyuroku (Japanese).
  • ``Schroedinger equation with point nonlinearity," Riccardo Adami, Reika Fukuizumi, Justin Holmer Oberwolfach Report (2017)
  • Thesis

  • "Stability and instability of standing waves for nonlinear Scrödinger equations," Tohoku Mathematical Publications 25, (2003), 68 pages PDF file