Sharp ill-posedness result for the periodic Benjamin-Ono equation

  • Molinet L
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Abstract

We prove the discontinuity for the weak L2(T)-topology of the flow-map associated with the periodic Benjamin-Ono equation. This ensures that this equation is ill-posed in Hs(T) as soon as s < 0 and thus completes exactly the well-posedness result obtained in Molinet (2008) [12]. © 2009 Elsevier Inc. All rights reserved.

Author-supplied keywords

  • Benjamin-Ono equation
  • Cauchy problem
  • Continuity with respect to initial data
  • Ill-posedness result

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Authors

  • Luc Molinet

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