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Isaac Scientific Publishing
New Horizons in Mathematical Physics
Prof. Nakao Hayashi,  Osaka University, Japan
Department of Mathematics
Graduate School of Science, Osaka University
Toyonaka, Osaka 560-0043, Japan
JAPAN
Research Interests
On asymptotic behavior in time of solutions to nonlinear dispersive wave equations including Nonlinear Schrodinger, Klein-Gordon, Benjamin-Ono or Korteweg-de Vries equations Basic analysis
Selected Publication List
• N.Hayashi, Classical solutions of nonlinear Schrodinger equations, Manuscripta Math. 55(1986), pp. 171-190.
• N.Hayashi, K.Nakamitsu and M.Tsutsumi, On solutions of the initial value problem for nonlinear Schrodinger equations, J. Funct. Anal., 71(1987), pp. 218-245.
• N.Hayashi and W. von Wahl, On the global strong solutions of coupled Klein-Gordon Schrodinger equations, J. Math. Soc. Japan, 39(1987), pp. 489-499.
• N.Hayashi and T.Ozawa, Time decay of solutions to the Cauchy problem for time-dependent Schrodinger-Hartree equations, Commun. Math. Phys., 110(1987), pp. 467-478.
• N.Hayashi, Global existence of small analytic solutions to nonlinear Schodinger equations, Duke Math. J., 60(1990), pp.717-727.
• N.Hayashi, The initial value problem for the derivative nonlinear Schodinger equations in the energy space, J.Nonlinear Anal. T.M.A., 20(1993), pp. 823-833.
• N.Hayashi and K.Kato, Regularity in time of solutions to nonlinear Schrodinger equations, J. Funct. Anal.,128(1995), pp. 253-277.
• J.Ginibre and N.Hayashi, Almost global existence of small solutions to quadratic nonlinear Schrodinger equations in three space dimensions}, Math. Z., 219(1995), pp. 119-140.
• N.Hayashi, Global existence of small solutions to quadratic nonlinear wave equations in an exterior domain, J.Funct. Anal., 131(1995), pp. 302-344.
• N.Hayashi and P.I.Naumkin, Asymptotics in large time of solutions to nonlinear Schrodinger and Hartree equations, Amer. J. Math., 120(1998), pp. 369-389.
• N.Hayashi and P.I.Naumkin, Large time asymptotics of solutions to the generalized Korteweg-de Vries equation, J.Funct.Anal., 159(1998), pp. 110-136.
• N.Hayashi, E.I.Kaikina and P.I.Naumkin, Global existence and time decay of small solutions to the Landau-Ginzburg type equations, J.Analyse Mathematique, 90(2003), pp. 141-173.
• N.Hayashi, E.I.Kaikina and P.I.Naumkin, Damped wave equation with a critical nonlinearity, Trans. Amer. Math. Soc., 358(2006), pp. 1165-1185.
• N.Hayashi and P.I.Naumkin, Domain and range of the modified wave operator for Schrodinger equations with a critical nonlinearity, Comm. Math. Phys., 267(2006), pp. 477-492.
• N.Hayashi and P.I.Naumkin, Scattering operator for the nonlinear Klein-Gordon equations in higher space dimensions, J. Differential Equations, 244(2008), pp. 188-199.
• N.Hayashi, C. Li and P.I.Naumkin, On a system of nonlinear Schrodinger equations in 2d, Differential and Integral Equations, 24(2011), pp. 417-434.
• N.Hayashi and P. Naumkin, Logarithmic time decay for cubic nonlinear Schrodinger equations, International Mathematics Research Notices, 2014, rnu102, 40 pages.
• N.Hayashi and P. Naumkin, Large time asymptotics for the reduced Ostrovsky equation, Commun. Math. Phys., 335(2015),no.2, April, 713-738.
• N.Hayashi, C. Li and P.I. Naumkin, Nonlinear Schrodinger systems in 2d with nondecaying final data, J. Differential Equations 260(2016), no. 2, 1472-1495.
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