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Preprint (Author's original)arXiv.org - Non-exclusive license to distribute, Open
Preprint
Existence and analyticity of solutions of the Kuramoto-Sivashinsky equation with singular data
15 Aug 2023
Abstract
We prove existence of solutions to the Kuramoto-Sivashinsky equation with low-regularity data, in function spaces based on the Wiener algebra and in
pseudomeasure spaces. In any spatial dimension, we allow the data to have its antiderivative in the Wiener algebra. In one spatial dimension, we also allow data which is in a pseudomeasure space of negative order. In two spatial dimensions, we also allow data which is in a pseudomeasure space one derivative more regular than in the one-dimensional case. In the course of carrying out the existence arguments, we show a parabolic gain of regularity of the solutions as compared to the data. Subsequently, we show that the solutions are in fact analytic at any positive time in the interval of existence.
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Details
- Title
- Existence and analyticity of solutions of the Kuramoto-Sivashinsky equation with singular data
- Creators
- David M Ambrose - Drexel UniversityMilton C. Lopes Filho - Universidade Federal do Rio de JaneiroHelena J. Nussenzveig Lopes - Universidade Federal do Rio de Janeiro
- Resource Type
- Preprint
- Language
- English
- Academic Unit
- Mathematics
- Other Identifier
- 991020976218004721