The interplay between decay of the data and regularity of the solution in Schrödinger equations

DOI10.1007/s10231-019-00935-9zbMath1442.35361OpenAlexW2990114548MaRDI QIDQ778061

Alessia Ascanelli, Massimo Cicognani, Michael Reissig

Publication date: 30 June 2020

Published in: Annali di Matematica Pura ed Applicata. Serie Quarta (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10231-019-00935-9

zbMATH Keywords

Cauchy problemwell-posednessSchrödinger equationregularity of solutionspseudo-differential operators

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Pseudodifferential operators as generalizations of partial differential operators (35S05) Ill-posed problems for PDEs (35R25) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Time-dependent Schrödinger equations and Dirac equations (35Q41) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02)

Related Items (2)

The Cauchy problem for 3-evolution equations with data in Gelfand-Shilov spaces ⋮ Semilinear \(p\)-evolution equations in weighted Sobolev spaces

Cites Work

• Weighted energy estimates for \(p\)-evolution equations in \textit{SG} classes
• Some remarks on the Cauchy problem for Schrödinger type equations
• Commutator methods and a smoothing property of the Schrödinger evolution group
• The hyperbolic Cauchy problem
• Necessary conditions for the well-posedness of Schrödinger type equations in Gevrey spaces
• The Cauchy problem for Schrödinger type equations
• Schrödinger-type equations in Gelfand-Shilov spaces
• Unnamed Item

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