Global well-posedness and scattering of a 2D Schrödinger equation with exponential growth

zbMath1201.35178MaRDI QIDQ1959773

Tarek Saanouni

Publication date: 12 October 2010

Published in: Bulletin of the Belgian Mathematical Society - Simon Stevin (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/euclid.bbms/1284570731

zbMATH Keywords

scatteringwell-posednessnonlinear Schrödinger equationMoser-Trudinger inequality

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Critical exponents in context of PDEs (35B33) NLS equations (nonlinear Schrödinger equations) (35Q55) Schrödinger operator, Schrödinger equation (35J10) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Continuation and prolongation of solutions to PDEs (35B60) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02)

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Well-posedness issues for a class of coupled nonlinear Schrödinger equations with critical exponential growth ⋮ Global well-posedness of some high-order semilinear wave and Schrödinger type equations with exponential nonlinearity ⋮ A note on the inhomogeneous nonlinear heat equation in two space dimensions ⋮ Blowing-up semilinear wave equation with exponential nonlinearity in two space dimensions ⋮ A note on strong instability of standing waves for some semilinear wave and heat equations ⋮ A note on the instability of a focusing nonlinear damped wave equation ⋮ A note on the critical nonlinear high-order Schrödinger equation ⋮ A blowing up wave equation with exponential type nonlinearity and arbitrary positive energy ⋮ Scattering of a 2D Schrödinger equation with exponential growth in the conformal space ⋮ Global well-posedness of a damped Schrödinger equation in two space dimensions ⋮ Global well-posedness of some high-order focusing semilinear evolution equations with exponential nonlinearity ⋮ Global well-posedness and instability of an inhomogeneous nonlinear Schrödinger equation ⋮ A note on global well-posedness and blow-up of some semilinear evolution equations

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