Unconditional uniqueness for the modified Korteweg–de Vries equation on the line

• Luc Molinet ^[1] ; Didier Pilod ^[2] ; Stéphane Vento ^[3]
  1. [1] François Rabelais University

     François Rabelais University

     Arrondissement de Tours, Francia

     
  2. [2] University of Bergen

     University of Bergen

     Noruega

     
  3. [3] Paris 13 University

     Paris 13 University

     Arrondissement de Saint-Denis, Francia

     

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• Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 34, Nº 4, 2018, págs. 1563-1608
• Idioma: inglés
• Texto completo no disponible (Saber más ...)
• Resumen

  • We prove that the modified Korteweg–de Vries (mKdV) equation is unconditionally well-posed in Hs(R) for s>1/3. Our method of proof combines the improvement of the energy method introduced recently by the first and third authors with the construction of a modified energy. Our approach also yields a priori estimates for the solutions of mKdV in Hs(R), for s>0, and enables us to construct weak solutions at this level of regularity.