Near soliton dynamics and singularity formation for $L^2$ critical problems

Abstract

This survey reviews the state of the art concerning the singularity formation for two canonical dispersive problems: the mass critical non linear Schrödinger equation and the mass critical generalized KdV equation. In particular, we address the question of the classification of the flow for initial data near the soliton.

References in corpus (7)

• Global well-posedness, scattering and blow-up for the energy-critical, focusing, non-linear Schrodinger equation in the radial case
• Renormalization and blow up for charge one equivariant critical wave maps
• Nondispersive solutions to the L2-critical half-wave equation
• Stable blow up dynamics for the 1-corotational energy critical harmonic heat flow
• Asymptotic stability, concentration, and oscillation in harmonic map heat-flow, Landau-Lifshitz, and Schroedinger maps on R^2
• Minimal blow-up solutions to the mass-critical inhomogeneous NLS equation
• On collapsing ring blow up solutions to the mass supercritical NLS

Cited by in corpus (2)

• Construction of type II blow-up solutions for the energy-critical wave equation in dimension 5
• Stable shock formation for nearly simple outgoing plane symmetric waves