Global existence of solutions for a fourth-order nonlinear Schrödinger equation in \(n+1\) dimensions

DOI10.1016/j.na.2010.03.052zbMath1191.35253OpenAlexW1555615203MaRDI QIDQ975854

Cuihua Guo

Publication date: 11 June 2010

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.na.2010.03.052

zbMATH Keywords

Cauchy problemglobal existenceI-methodfourth-order Schrödinger equation

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) NLS equations (nonlinear Schrödinger equations) (35Q55) Existence problems for PDEs: global existence, local existence, non-existence (35A01)

Related Items (6)

On the management fourth-order Schrödinger-Hartree equation ⋮ Global well-posedness for a \(L^2\)-critical nonlinear higher-order Schrödinger equation ⋮ Global existence and asymptotic behavior of the Cauchy problem for fourth-order Schrödinger equations with combined power-type nonlinearities ⋮ Finite dimensional global attractor for a dissipative anisotropic fourth order Schrödinger equation ⋮ Global existence and scattering for a class of nonlinear fourth-order Schrödinger equation below the energy space ⋮ The initial-boundary value problem for the biharmonic Schrödinger equation on the half-line

Cites Work

• Well-posedness of higher-order nonlinear Schrödinger equations in Sobolev spaces \(H^{s}(\mathbb R^{n})\) and applications
• Global well-posedness for energy critical fourth-order Schrödinger equations in the radial case
• Global well-posedness and scattering for the focusing energy-critical nonlinear Schrödinger equations of fourth order in the radial case
• Stability of solitons described by nonlinear Schrödinger-type equations with higher-order dispersion
• Multilinear estimates for periodic KdV equations, and applications
• Global existence of solutions for a fourth-order nonlinear Schrödinger equation
• Global existence for semilinear Schrödinger equations in \(2+1\) dimensions
• Global well-posedness and scattering for the energy-critical Schrödinger equation in \(\mathbb R^{3}\)
• Self-Focusing with Fourth-Order Dispersion
• Dispersion estimates for fourth order Schrödinger equations

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