Global well-posedness on the derivative nonlinear Schrödinger equation revisited

Abstract

As a continuation of the previous work \cite{Wu}, we consider the global well-posedness for the derivative nonlinear Schrödinger equation. We prove that it is globally well-posed in energy space, provided that the initial data $u_0\in H^1(\mathbb{R})$ with $\Vert u_0{\Vert }_{L^2}<2\sqrt{\pi }$.

8 pages. Some typos are corrected

References in corpus (2)

• Low regularity local well-posedness of the Derivative Nonlinear Schrödinger Equation with periodic initial data
• Global well-posedness for Schrödinger equation with derivative in $H^{1/2}(\mathbb{R})$

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• On the well-posedness problem for the derivative nonlinear Schrödinger equation
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• Small data well-posedness for derivative nonlinear Schrödinger equations
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• A priori estimates for the derivative nonlinear Schrödinger equation
• Traveling waves for a nonlinear Schrödinger system with quadratic interaction
• Long-time asymptotic behavior of a mixed schrödinger equation with weighted Sobolev initial data
• Long-period limit of exact periodic traveling wave solutions for the derivative nonlinear Schrödinger equation
• Global Existence for the Derivative Nonlinear Schrodinger Equation by the Method of Inverse Scattering
• Stability of algebraic solitons for nonlinear Schrödinger equations of derivative type: variational approach
• Existence of global solutions to the derivative NLS equation with the inverse scattering transform method
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• Orbital stability of solitary waves for generalized derivative nonlinear Schrödinger equations in the endpoint case
• Derivative non-linear Schrödinger equation: Singular manifold method and Lie symmetries
• Solitary waves for nonlinear Schrödinger equation with derivative
• Optimal small data Scattering for the generalized derivative nonlinear Schrödinger equations
• Self-similar solutions to the derivative nonlinear Schrödinger equation
• The stability of degenerate solitons for derivative nonlinear Schrodinger equations
• Instability of degenerate solitons for nonlinear Schrödinger equations with derivative