On Schrödinger systems with cubic dissipative nonlinearities of derivative type

Abstract

Consider the initial value problem for systems of cubic derivative nonlinear Schrödinger equations in one space dimension with the masses satisfying a suitable resonance relation. We give structural conditions on the nonlinearity under which the small data solution gains an additional logarithmic decay as $t\to +\infty$ compared with the corresponding free evolution.

26 pages

References in corpus (3)

• Well-posedness and scattering for a system of quadratic derivative nonlinear Schrödinger equations with low regularity initial data
• Energy decay for systems of semilinear wave equations with dissipative structure in two space dimensions
• Null structure in a system of quadratic derivative nonlinear Schrödinger equations

Cited by in corpus (7)

• Large time asymptotics for a cubic nonlinear Schrödinger system in one space dimension
• The lifespan of small solutions to cubic derivative nonlinear Schrödinger equations in one space dimension
• On Agemi-type structural conditions for a system of semilinear wave equations
• Large time asymptotics for a cubic nonlinear Schrödinger system in one space dimension, II
• On the scattering problem for the nonlinear Schrödinger equation with a potential in 2D
• On the derivative nonlinear Schrödinger equation with weakly dissipative structure
• On the decay estimate for small solutions to nonlinear Klein-Gordon equations with dissipative structure