The lifespan of small solutions to cubic derivative nonlinear Schrödinger equations in one space dimension

Abstract

Consider the initial value problem for cubic derivative nonlinear Schrödinger equations in one space dimension. We provide a detailed lower bound estimate for the lifespan of the solution, which can be computed explicitly from the initial data and the nonlinear term. This is an extension and a refinement of the previous work by one of the authors where the gauge-invariant nonlinearity was treated.

19 pages

References in corpus (2)

• Scattering and small data completeness for the critical nonlinear Schroediger equation
• On Schrödinger systems with cubic dissipative nonlinearities of derivative type

Cited by in corpus (5)

• Asymptotic behavior of solutions to nonlinear Schrödinger equations with time-dependent harmonic potentials
• Almost global existence for cubic nonlinear Schrödinger equations in one space dimension
• Remarks on derivative nonlinear Schrödinger systems with multiple masses
• On the derivative nonlinear Schrödinger equation with weakly dissipative structure
• Energy decay for small solutions to semilinear wave equations with weakly dissipative structure