×

On the local smoothing for a class of conformally invariant Schrödinger equations. (English) Zbl 1171.35117

The authors consider the Cauchy problems for certain linear and semilinear Schrödinger equations having the feature of being invariant under the conformal transformation. They prove a priori estimates from above and from below for solutions, which show a phenomenon of gain of \(\frac{1}{2}\) a derivative during the evolution. The techniques involved in the proves can be also used to obtain some new uniqueness results.

MSC:

35Q55 NLS equations (nonlinear Schrödinger equations)
81U30 Dispersion theory, dispersion relations arising in quantum theory
35B45 A priori estimates in context of PDEs
35B65 Smoothness and regularity of solutions to PDEs
PDFBibTeX XMLCite
Full Text: DOI arXiv