Smoothing effect for time-degenerate Schrödinger operators

Abstract

In this work we consider an example of a linear time-degenerate Schrödinger operator. We show that with the appropriate assumptions the operator satisfies a Kato smoothing effect. We also show that the solutions to the nonlinear initial value problems involving this operator and polynomial derivative nonlinearities are locally well-posed and their solutions also satisfy the same smoothing estimates as the linear solutions.

References in corpus (1)

• Quasilinear Schrödinger equations III: Large Data and Short Time

Cited by in corpus (3)

• On the uniqueness of variable coefficient Schrödinger equations
• Smoothing and Strichartz estimates for degenerate Schrödinger-type equations
• Sharp Strichartz estimates for some variable coefficient Schrödinger operators on $\mathbb{R}\times {\mathbb{T}}^2$