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Existence and Uniqueness of Low Regularity Solutions for the Dullin-Gottwald-Holm Equation

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Abstract

We establish the local existence and uniqueness of solutions for the Dullin-Gottwald-Holm equation with continuously differentiable, periodic initial data. The regularity conditions needed for the Cauchy problem via the semigroup approach of quasilinear hyperbolic equations of evolution or the viscosity method are significantly lowered.

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Authors and Affiliations

  1. Department of Mathematics, University of Craiova, Al. I Cuza 13, Craiova, Romania

    Octavian G. Mustafa

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  1. Octavian G. Mustafa
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Correspondence to Octavian G. Mustafa.

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Communicated by A. Kupiainen

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Mustafa, O. Existence and Uniqueness of Low Regularity Solutions for the Dullin-Gottwald-Holm Equation. Commun. Math. Phys. 265, 189–200 (2006). https://doi.org/10.1007/s00220-006-1532-9

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  • DOI: https://doi.org/10.1007/s00220-006-1532-9

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