Unconditional well-posedness for the periodic Boussinesq and Kawahara equations

Dan-Andrei Geba; Dan-Andrei Geba

doi:10.3934/era.2024052

Electronic Research Archive

2024, Volume 32, Issue 2: 1067-1081. doi: 10.3934/era.2024052

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Unconditional well-posedness for the periodic Boussinesq and Kawahara equations

Dan-Andrei Geba ^,

Department of Mathematics, University of Rochester, Rochester, NY 14627, USA

Received: 11 December 2023 Revised: 05 January 2024 Accepted: 11 January 2024 Published: 25 January 2024

In this article, we obtain new results on the unconditional well-posedness for a pair of periodic nonlinear dispersive equations using an abstract framework introduced by Kishimoto. This framework is based on a normal form reductions argument coupled with a number of crucial multilinear estimates.
- Boussinesq equation,
- Kawahara equation,
- well-posedness,
- unconditional uniqueness,
- normal form
Citation: Dan-Andrei Geba. Unconditional well-posedness for the periodic Boussinesq and Kawahara equations[J]. Electronic Research Archive, 2024, 32(2): 1067-1081. doi: 10.3934/era.2024052

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Abstract

In this article, we obtain new results on the unconditional well-posedness for a pair of periodic nonlinear dispersive equations using an abstract framework introduced by Kishimoto. This framework is based on a normal form reductions argument coupled with a number of crucial multilinear estimates.

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