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On the Korteweg-de Vries equation

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Abstract

Existence, uniqueness, and continuous dependence on the initial data are proved for the local (in time) solution of the (generalized) Korteweg-de Vries equation on the real line, with the initial function ϕ in the Sobolev space of order s>3/2 and the solution u(t) staying in the same space, s=∞ being included For the proper KdV equation, existence of global solutions follows if s≥2. The proof is based on the theory of abstract quasilinear evolution equations developed elsewhere.

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Authors and Affiliations

  1. Department of Mathematics, University of California, 94720, Berkeley, CA, USA

    Tosio Kato

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  1. Tosio Kato
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Additional information

Dedicated to Hans Lewy and Charles B. Morrey Jr.

Partially supported by NSF Grant MCS76-04655.

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Kato, T. On the Korteweg-de Vries equation. Manuscripta Math 28, 89–99 (1979). https://doi.org/10.1007/BF01647967

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  • DOI: https://doi.org/10.1007/BF01647967

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