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Functional Analysis and Its Applications

, Volume 46, Issue 4, pp 279–286 | Cite as

On the nonexistence of global solutions of the Cauchy problem for the Korteweg-de Vries Equation

  • S. I. Pokhozhaev
Article
  • 109 Downloads

Abstract

We establish conditions on the initial data under which the Cauchy problem for the Korteweg-de Vries equation does not admit a solution global in t > 0. The proof of the results is based on the nonlinear capacity method [7]. In closing, we provide an example.

Key words

blow-up KdV equation initial-boundary value problem Cauchy problem nonlinear capacity 

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Copyright information

© Springer Science+Business Media New York 2012

Authors and Affiliations

  1. 1.Steklov Institute of MathematicsRussian Academy of SciencesMoscowRussia

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