Global rough solutions to the critical generalized KdV equation

Abstract

We prove that the initial value problem (IVP) for the critical generalized KdV equation $u_t+u_{xxx}+(u^5{)}_x=0$ on the real line is globally well-posed in $H^s(\mathbb{R})$ provided $s>3/5$.

23 pages, no figures. References updated, some comments added after Proposition 3.1, typos fixed. Submitted for publication

References in corpus (3)

• The low regularity global solutions for the critical generalized KdV equation
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• A remark on global well-posedness below L^2 for the gKdV-3 equation

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• Global well-posedness for low regularity data in the 2d modified Zakharov-Kuznetsov equation
• The low regularity global solutions for the critical generalized KdV equation
• Large data scattering for the defocusing supercritical generalized KdV equation
• Nonlinear Profile Decomposition and the Concentration Phenomenon for Supercritical Generalized KdV Equations
• Singularity for Solutions of Linearized KdV Equations
• On the mass-critical generalized KdV equation
• Global well-posedness for periodic generalized KdV equation
• Global Well-Posedness for a Coupled Modified KdV System