On \(L^ 2\) well posedness of the Cauchy problem for Schrödinger type equations on the Riemannian manifold and the Maslov theory

DOI10.1215/S0012-7094-88-05623-2zbMath0713.58055MaRDI QIDQ749976

Wataru Ichinose

Publication date: 1988

Published in: Duke Mathematical Journal (Search for Journal in Brave)

zbMATH Keywords

Cauchy problemRiemann manifoldMaslov constructionSchrödinger type equations

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Schrödinger operator, Schrödinger equation (35J10) Propagation of singularities; initial value problems on manifolds (58J47)

Related Items

The general quasilinear ultrahyperbolic Schrödinger equation, Smoothing effects of Schrödinger evolution groups on Riemannian manifolds, Remarks on the cauchy problem for schrödinger-type equations, Quasilinear Schrödinger equations. I: Small data and quadratic interactions, On the local-energy decay property for the elastic wave equation with the Neumann boundary condition, Quasilinear Schrödinger equations. II: Small data and cubic nonlinearities, The initial value problem for a third order dispersive equation on the two-dimensional torus, Quasilinear Schrödinger equations. III: Large data and short time., Variable coefficient Schrödinger flows for ultrahyperbolic operators

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