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Well-posedness and regularity of the fifth order Kadomtsev–Petviashvili I equation in the analytic Bourgain spaces

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Abstract

The paper is devoted to study a Cauchy problem for fifth-order Kadomtsev–Petviashvili I equation. With data in analytic Bourgain spaces on the line and the circle, we prove that the problem is well posed. We also treat the regularity in t and x, y, where the solution is analytic in x, y and belongs to \(G^{5 }\) in t.

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Acknowledgements

The authors wish to thank deeply the anonymous referee for his/her useful remarks and his/her careful reading of the proofs presented in this paper.

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Authors and Affiliations

  1. Laboratoire de Mathématiques et Sciences appliquées, Université de Ghardaia, Metlili, Algerie

    A. Boukarou & K. Guerbati

  2. Department of Mathematics, College of Sciences and Arts, Qassim University, Al-Ras, Kingdom of Saudi Arabia

    Kh. Zennir

  3. Department of Differential Equations, Faculty of Mathematics and Informatics, University of Sofia, Sofia, Bulgaria

    G. G. Svetlin

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  1. A. Boukarou
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  2. Kh. Zennir
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  3. K. Guerbati
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  4. G. G. Svetlin
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Correspondence to Kh. Zennir.

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Boukarou, A., Zennir, K., Guerbati, K. et al. Well-posedness and regularity of the fifth order Kadomtsev–Petviashvili I equation in the analytic Bourgain spaces. Ann Univ Ferrara 66, 255–272 (2020). https://doi.org/10.1007/s11565-020-00340-8

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  • DOI: https://doi.org/10.1007/s11565-020-00340-8

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