Remarks on derivative nonlinear Schr\"odinger systems with multiple masses

We prove global existence of small solutions to the initial value problem for a class of cubic derivative nonlinear Schr\"odinger systems with the masses satisfying suitable non-resonance relations. The large-time asymptotics of the solutions are also shown. This work is intended to provide a counterpart of the previous paper (arXiv:1507.07617) in which the mass resonance case was treated.

[1]  Hideaki Sunagawa,et al.  The lifespan of small solutions to cubic derivative nonlinear Schrödinger equations in one space dimension , 2015, 1511.03126.

[2]  Chunhua Li,et al.  On Schrödinger systems with cubic dissipative nonlinearities of derivative type , 2015, 1507.07617.

[3]  Hiroyuki Hirayama.  Well-posedness and scattering for a system of quadratic derivative nonlinear Schr\"odinger equations with low regularity initial data , 2013, 1309.4336.

[4]  N. Hayashi,et al.  On a system of nonlinear Schrödinger equations with quadratic interaction , 2013 .

[5]  M. Ikeda,et al.  Null Structure in a System of Quadratic Derivative Nonlinear Schrödinger Equations , 2013, 1305.3662.

[6]  Chunhua Li,et al.  A remark on decay rates of solutions for a system of quadratic nonlinear Schrödinger equations in 2D , 2013, Differential and Integral Equations.

[7]  Tohru Ozawa,et al.  Small data blow-up for a system of nonlinear Schrödinger equations , 2012, 1210.0606.

[8]  Chunhua Li,et al.  Decay of solutions for a system of nonlinear Schrödinger equations in 2D , 2012 .

[9]  N. Hayashi,et al.  Modified Wave Operator for a System of Nonlinear Schrödinger Equations in 2d , 2012 .

[10]  S. Katayama,et al.  A note on the null condition for quadratic nonlinear Klein‐Gordon systems in two space dimensions , 2011, 1105.1952.

[11]  N. Hayashi,et al.  On a system of nonlinear Schrödinger equations in 2d , 2011, Differential and Integral Equations.

[12]  Yuichiro Kawahara,et al.  Global small amplitude solutions for two-dimensional nonlinear Klein-Gordon systems in the presence of mass resonance , 2011, 1104.1354.

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

[14]  Hideaki Sunagawa.  Large time asymptotics of solutions to nonlinear Klein-Gordon systems , 2005 .

[15]  Jean-Marc Delort,et al.  Global existence of small solutions for quadratic quasilinear Klein–Gordon systems in two space dimensions , 2004 .

[16]  Thierry Colin,et al.  On a quasilinear Zakharov system describing laser-plasma interactions , 2004, Differential and Integral Equations.

[17]  Hideaki Sunagawa.  On global small amplitude solutions to systems of cubic nonlinear Klein-Gordon equations with different mass terms in one space dimension , 2003 .

[18]  N. Hayashi,et al.  On the reduction of the modified Benjamin-Ono equation to the cubic derivative nonlinear Schrödinger equation , 2001 .

[19]  N. Hayashi,et al.  Smoothing effects for some derivative nonlinear Schrödinger equations without smallness condition , 1999, SUT Journal of Mathematics.

[20]  Nakao Hayashi,et al.  Asymptotics for large time of solutions to the nonlinear Schrödinger and Hartree equations , 1998 .

[21]  C. H. Li,et al.  SMALL DATA SCATTERING FOR A SYSTEM OF NONLINEAR SCHR ¨ ODINGER EQUATIONS , 2011 .

[22]  P. Geramain,et al.  GLOBAL SOLUTIONS FOR 3D QUADRATIC SCHRÖDINGER EQUATIONS , 2008 .

[23]  Y. Tsutsumi.  Stability of Constant Equilibrium for the Maxwell-Higgs Equations , 2003 .

[24]  Nakao Hayashi,et al.  Large time asymptotics of solutions to the generalized Benjamin-Ono equation , 1999 .