Quasilinear Schrödinger equations. I: Small data and quadratic interactions

DOI10.1016/j.aim.2012.06.010zbMath1248.35196arXiv1106.0490OpenAlexW2146852422MaRDI QIDQ452062

Daniel Tataru, Jason Metcalfe, Jeremy L. Marzuola

Publication date: 19 September 2012

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1106.0490

zbMATH Keywords

Schrödinger equationslocal existence theory

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) NLS equations (nonlinear Schrödinger equations) (35Q55)

Related Items

Local well-posedness for quasi-linear problems: A primer ⋮ The dual approach to stationary and evolution quasilinear PDEs ⋮ Local well-posedness for a quasilinear Schroedinger equation with degenerate dispersion ⋮ Global transversal stability of Euclidean planes under skew mean curvature flow evolutions ⋮ Local well-posedness of the skew mean curvature flow for small data in \(d \geqq 2\) dimensions ⋮ Well-posedness and smoothing effect for generalized nonlinear Schrödinger equations ⋮ Quasilinear Schrödinger equations. II: Small data and cubic nonlinearities ⋮ Wellposedness of some quasi-linear Schrödinger equations ⋮ Smoothing effect for time-degenerate Schrödinger operators ⋮ Well-posedness of fully nonlinear KdV-type evolution equations ⋮ Local well-posedness for the quasi-linear Hamiltonian Schrödinger equation on tori ⋮ Quasilinear Schrödinger equations. III: Large data and short time. ⋮ Global and local theory of skew mean curvature flows ⋮ Large data local well-posedness for a class of KdV-type equations ⋮ Local well-posedness of skew mean curvature flow for small data in \(d\ge 4\) dimensions

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