Periodic Korteweg de Vries equation with measures as initial data

• J. Bourgain ^[1]
  1. [1] School of Mathematics, USA
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 3, Nº. 2, 1997, págs. 115-159
• Idioma: inglés
• DOI: 10.1007/s000290050008
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• Resumen

  • The main result of the paper is that the periodic KdV equation yt+∂3xy+yyx=0 has a unique global solution for initial data y(0) given by a measure μ∈M(T) of sufficiently small norm ∥μ∥ . There are two main ingredients in the proof. The first is the study of the local well-posedness problem in terms of the space-time Fourier-norms as exploited in [Bo] and also subsequent work such as [K-P-V2]. At the end the estimates eventually depend on a uniform estimate in terms of the Fourier coefficients¶¶ supn∈Z,t∈R|y^(n)(t)|