On the inhomogeneous biharmonic nonlinear Schrödinger equation: local, global and stability results

DOI10.1016/j.nonrwa.2020.103174zbMath1451.35185arXiv1910.03908OpenAlexW3036340784MaRDI QIDQ2208776

Carlos M. Guzmán, Ademir Pastor Ferreira

Publication date: 4 November 2020

Published in: Nonlinear Analysis. Real World Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1910.03908

zbMATH Keywords

global well-posednesslocal well-posednessstability theoryinhomogeneous biharmonic nonlinear Schrödinger equation

Mathematics Subject Classification ID

NLS equations (nonlinear Schrödinger equations) (35Q55) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Biharmonic, polyharmonic functions and equations, Poisson's equation in two dimensions (31A30) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02) Strong solutions to PDEs (35D35)

Related Items

Ground state solution to the biharmonic equation ⋮ Global well-posedness and critical norm concentration for inhomogeneous biharmonic NLS ⋮ Scattering for the non-radial inhomogenous biharmonic NLS equation ⋮ Some remarks on the inhomogeneous biharmonic NLS equation ⋮ Non-radial finite time blow-up for the fourth-order nonlinear Schrödinger equations ⋮ Local well-posedness of a critical inhomogeneous bi-harmonic Schrödinger equation ⋮ Energy scattering for non-radial inhomogeneous fourth-order Schrödinger equations ⋮ Random data final-state problem of fourth-order inhomogeneous NLS ⋮ Small data global well-posedness for the inhomogeneous biharmonic NLS in Sobolev spaces ⋮ Energy scattering for radial focusing inhomogeneous bi-harmonic Schrödinger equations ⋮ Bilinear Strichartz's type estimates in Besov spaces with application to inhomogeneous nonlinear biharmonic Schrödinger equation ⋮ A note on the inhomogeneous fourth-order Schrödinger equation ⋮ Local well-posedness for the inhomogeneous biharmonic nonlinear Schrödinger equation in Sobolev spaces ⋮ Scattering for radial defocusing inhomogeneous bi-harmonic Schrödinger equations

Cites Work

• Global well-posedness and blow-up on the energy space for the inhomogeneous nonlinear Schrödinger equation
• On the well-posedness for stochastic fourth-order Schrödinger equations
• Scattering for the radial 3D cubic focusing inhomogeneous nonlinear Schrödinger equation
• Global well-posedness and scattering for the defocusing energy-critical nonlinear Schrödinger equations of fourth order in dimensions \(d\geqslant 9\)
• Functional spaces for the theory of elliptic partial differential equations. Transl. from the French by Reinie Erné
• Scattering for the focusing energy-subcritical nonlinear Schrödinger equation
• An inhomogeneous, \(L^2\)-critical, nonlinear Schrödinger equation
• The focusing energy-critical fourth-order Schrödinger equation with radial data
• Global well-posedness, scattering and blow-up for the energy-critical, focusing, nonlinear Schrö\-dinger equation in the radial case
• Global well-posedness for energy critical fourth-order Schrödinger equations in the radial case
• Schrödinger equations with a spatially decaying nonlinearity: existence and stability of standing waves
• The cubic fourth-order Schrödinger equation
• 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
• Energy scattering for a class of the defocusing inhomogeneous nonlinear Schrödinger equation
• Scattering for the radial focusing inhomogeneous NLS equation in higher dimensions
• Global existence of small solutions for the fourth-order nonlinear Schrödinger equation
• On well posedness for the inhomogeneous nonlinear Schrödinger equation
• A sharp condition for scattering of the radial 3D cubic nonlinear Schrödinger equation
• Scattering of solutions to the fourth-order nonlinear Schrödinger equation
• Scattering for the focusingL²-supercritical andḢ²-subcritical biharmonic NLS equations
• FINITE TIME BLOWUP FOR THE FOURTH-ORDER NLS
• Scattering theory for the fourth-order Schrödinger equation in low dimensions
• Self-Focusing with Fourth-Order Dispersion
• Interpolation inequalities with weights
• Introduction to nonlinear dispersive equations
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