Formation of singularities in nonlinear dispersive PDEs

  • Galina Perelman

    Laboratoire d’Analyse et de Mathématiques Appliquées UMR 8050, Université Paris-Est Créteil, 61 avenue du Général de Gaulle, 94010 Créteil Cedex, France
Formation of singularities in nonlinear dispersive PDEs cover
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This contribution addresses the problem of singularity formation in nonlinear dispersive equations. Despite significant progress made in the last 20 years, for most even simplest canonical models our understanding of the question is far from being complete. The aim of this note is to give a selection of results and open questions illustrating the present state of the problem in the context of some basic model equations, mostly of Schrödinger type, such as the semilinear Schrödinger and Schrödinger map equations, putting an emphasis on the role of solitons in the mechanisms of singularity formation.