GLOBAL WELL-POSEDNESS FOR THE GENERALISED FOURTH-ORDER SCHRÖDINGER EQUATION

DOI10.1017/S0004972711003327zbMath1247.35053MaRDI QIDQ2891966

Yu-Zhao Wang

Publication date: 18 June 2012

Published in: Bulletin of the Australian Mathematical Society (Search for Journal in Brave)

Mathematics Subject Classification ID

NLS equations (nonlinear Schrödinger equations) (35Q55) Variational methods for second-order elliptic equations (35J20) Quasielliptic equations (35H30) Positive solutions to PDEs (35B09) Quasilinear elliptic equations with (p)-Laplacian (35J92)

Related Items (12)

Global existence of small solutions for the fourth-order nonlinear Schrödinger equation ⋮ The probabilistic Cauchy problem for the fourth order Schrödinger equation with special derivative nonlinearities ⋮ Retracted: The probabilistic Cauchy problem for the fourth order Schrödinger equation with special derivative nonlinearities ⋮ Well‐posedness of generalized KdV and one‐dimensional fourth‐order derivative nonlinear Schrödinger equations for data with an infinite L² norm ⋮ Factorization technique for the fourth-order nonlinear Schrödinger equation ⋮ Large time asymptotics for the fourth-order nonlinear Schrödinger equation ⋮ Global existence of small solutions for a quadratic nonlinear fourth-order Schrödinger equation in six space dimensions ⋮ Global existence and asymptotic behavior of solutions to the fourth-order nonlinear Schrödinger equation in the critical case ⋮ Asymptotics for the fourth-order nonlinear Schrödinger equation in the critical case ⋮ Well-posedness for the fourth-order Schrödinger equation with third order derivative nonlinearities ⋮ Global solution for a sixth-order nonlinear Schrödinger equation ⋮ Well-posedness and scattering for fourth order nonlinear Schrödinger type equations at the scaling critical regularity

Cites Work

• Unnamed Item
• Well-posedness results for the generalized Benjamin-Ono equation with small initial data.
• Global existence of solutions for a fourth-order nonlinear Schrödinger equation
• The Cauchy problem for the fourth-order nonlinear Schrödinger equation related to the vortex filament
• Wellposedness for the fourth order nonlinear Schrödinger equations
• The cauchy problem for the critical nonlinear Schrödinger equation in Hs
• Note on a modification to the nonlinear Schrödinger equation for application to deep water waves
• Well‐posedness and scattering results for the generalized korteweg‐de vries equation via the contraction principle

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