Global well-posedness for nonlinear schrodinger equations with energy-critical damping

We consider the Cauchy problem for the nonlinear Schrodinger equations with energy-critical damping. We prove the existence of global in-time solutions for general initial data in the energy space. Our results extend some results from [1, 2].

[1]  T. Tao.  Nonlinear dispersive equations : local and global analysis , 2006 .

[2]  G. Fibich,et al.  Nonlinear-damping continuation of the nonlinear Schr\"odinger equation - a numerical study , 2011, 1107.3281.

[3]  Weizhu Bao,et al.  Three-dimensional simulation of jet formation in collapsing condensates , 2004 .

[4]  Gadi Fibich,et al.  Self-Focusing in the Damped Nonlinear Schrödinger Equation , 2001, SIAM J. Appl. Math..

[5]  T. Cazenave.  Semilinear Schrodinger Equations , 2003 .

[6]  Christof Sparber,et al.  Global Well-Posedness for Cubic NLS with Nonlinear Damping , 2009, Communications in Partial Differential Equations.

[7]  Catherine Sulem,et al.  The nonlinear Schrödinger equation , 2012 .

[8]  Akihiro Shimomura,et al.  Asymptotic behavior of solutions to Schrödinger equations with a subcritical dissipative nonlinearity , 2007 .

[9]  C. Sulem,et al.  Linear versus nonlinear dissipation for critical NLS equation , 2005 .

[10]  Dun Zhao,et al.  The limit behavior of solutions for the nonlinear Schrodinger equation including nonlinear loss/gain with variable coefficient , 2013 .

[11]  Rémi Carles,et al.  Semi-classical Schrödinger equations with harmonic potential and nonlinear perturbation , 2003, math/0702656.

[12]  N. SIAMJ..  AN EXPLICIT UNCONDITIONALLY STABLE NUMERICAL METHOD FOR SOLVING DAMPED NONLINEAR SCHRÖDINGER EQUATIONS WITH A FOCUSING NONLINEARITY , 2003 .

[13]  Rémi Carles,et al.  Semi-Classical Analysis For Nonlinear Schrodinger Equations , 2008 .

[14]  Terence Tao,et al.  The Nonlinear Schrödinger Equation with Combined Power-Type Nonlinearities , 2005 .

[15]  Akihiro Shimomura,et al.  Asymptotic Behavior of Solutions for Schrödinger Equations with Dissipative Nonlinearities , 2006 .

[16]  Xiaoyi Zhang.  On the Cauchy problem of 3-D energy-critical Schrödinger equations with subcritical perturbations , 2006 .

[17]  Yu. Kagan,et al.  COLLAPSE AND BOSE-EINSTEIN CONDENSATION IN A TRAPPED BOSE GAS WITH NEGATIVE SCATTERING LENGTH , 1998 .