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.

Smoothing effect for time-degenerate Schrödinger operators

Federico, Serena
;
Staffilani, Gigliola
2021

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.
Federico, Serena; Staffilani, Gigliola
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11585/842243
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