Poincaré-Dulac Normal Form Reduction for Unconditional Well-Posedness of the Periodic Cubic NLS

[1]  J. Colliander,et al.  A remark on normal forms and the “upside-down” I-method for periodic NLS: Growth of higher Sobolev norms , 2010, 1010.2501.

[2]  Tadahiro Oh,et al.  On unconditional well-posedness of modified KdV , 2010, 1007.0270.

[3]  E. Titi,et al.  On the regularization mechanism for the periodic Korteweg–de Vries equation , 2009, 0910.1389.

[4]  Nader Masmoudi,et al.  Global Solutions for 3D Quadratic Schrödinger Equations , 2008, 1001.5158.

[5]  L. Molinet.  On ill-posedness for the one-dimensional periodic cubic Schrodinger equation , 2008, 0806.4538.

[6]  Axel Grünrock,et al.  Low Regularity Local Well-Posedness of the Derivative Nonlinear Schrödinger Equation with Periodic Initial Data , 2007, SIAM J. Math. Anal..

[7]  M. Christ.  POWER SERIES SOLUTION OF A NONLINEAR SCHR ¨ ODINGER EQUATION , 2005, math/0503368.

[8]  M. Christ.  Nonuniqueness of weak solutions of the nonlinear Schroedinger equation , 2005, math/0503366.

[9]  J. Bourgain.  A remark on normal forms and the “I-method” for periodic NLS , 2004 .

[10]  Jean Bourgain,et al.  Remarks on stability and diffusion in high-dimensional Hamiltonian systems and partial differential equations , 2004, Ergodic Theory and Dynamical Systems.

[11]  T. Tao,et al.  Instability of the periodic nonlinear Schrodinger equation , 2003, math/0311227.

[12]  J. Colliander,et al.  Asymptotics, frequency modulation, and low regularity ill-posedness for canonical defocusing equations , 2002, math/0203044.

[13]  Jean Bourgain,et al.  On nonlinear Schrödinger equations , 1998 .

[14]  Tosio Kato.  On nonlinear Schrödinger equations, II.HS-solutions and unconditional well-posedness , 1995 .

[15]  J. Bourgain,et al.  Fourier transform restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations , 1993 .

[16]  Jalal Shatah,et al.  Normal forms and quadratic nonlinear Klein‐Gordon equations , 1985 .

[17]  D. R. Heath-Brown,et al.  An Introduction to the Theory of Numbers, Sixth Edition , 2008 .

[18]  Y. Tsutsumi,et al.  Well-posedness of the Cauchy problem for the modified KdV equation with periodic boundary condition , 2004 .

[19]  G. Furioli,et al.  Unconditional well-posedness for semilinear Schrödinger and wave equations in H^s , 2003 .

[20]  P. Gérard,et al.  An instability property of the nonlinear Schrödinger equation on $S^{d}$ , 2002 .

[21]  Yi Zhou,et al.  Uniqueness of weak solution of the KdV equation , 1997 .

[22]  Vladimir Igorevich Arnold,et al.  Geometrical Methods in the Theory of Ordinary Differential Equations , 1983 .

[23]  E. T..  An Introduction to the Theory of Numbers , 1946, Nature.