BLOW-UP CRITERIA FOR LINEARLY DAMPED NONLINEAR SCHRODINGER EQUATIONS

We consider the Cauchy problem for linearly damped nonlinear Schrodinger equations i partial derivative(t)u + Delta u + iau = +/-vertical bar u vertical bar(alpha)u, (t, x) is an element of[0, infinity) x R-N, where a > 0 and alpha > 0. We prove the global existence and scattering for a sufficiently large damping parameter in the energy-critical case. We also prove the existence of finite time blow-up H-1 solutions to the focusing problem in the mass-critical and mass-supercritical cases.

Automated summary

In the Cauchy problem for linearly damped nonlinear Schrodinger equations, global existence and scattering are proven for a sufficiently large damping parameter in the energy-critical case, while the existence of finite time blow-up H-1 solutions is demonstrated for the focusing problem in the mass-critical and mass-supercritical cases.