Journal article
Existence and analyticity of solutions of the Kuramoto–Sivashinsky equation with singular data
Proceedings of the Royal Society of Edinburgh. Section A. Mathematics, pp 1-26
20 Nov 2024
Abstract
We prove the 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 that are in a pseudomeasure space of negative order. In two spatial dimensions, we also allow data that are 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 FilhoHelena J. Nussenzveig Lopes
- Publication Details
- Proceedings of the Royal Society of Edinburgh. Section A. Mathematics, pp 1-26
- Publisher
- CAMBRIDGE UNIV PRESS; CAMBRIDGE
- Number of pages
- 26
- Grant note
- National Science Foundation: DMS-1907684, DMS-2307638 CNPq: 304990/2022-1, 305309/2022-6 FAPERJ: E-26/201.209/2021, E-26/201.027/2022
D.M.A. gratefully acknowledges support from the National Science Foundation through grants DMS-1907684 and DMS-2307638. M.C.L.F. was partially supported by CNPq, through Grant # 304990/2022-1, and FAPERJ, through Grant # E-26/201.209/2021. H.J.N.L. acknowledges the support of CNPq, through Grant # 305309/2022-6, and of FAPERJ, through Grant # E-26/201.027/2022.
- Resource Type
- Journal article
- Language
- English
- Academic Unit
- Mathematics
- Web of Science ID
- WOS:001360840100001
- Scopus ID
- 2-s2.0-85210162518
- Other Identifier
- 991021965472004721
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- Collaboration types
- Domestic collaboration
- International collaboration
- Web of Science research areas
- Mathematics
- Mathematics, Applied