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Journal article
Global Solutions of the Two-Dimensional Kuramoto–Sivashinsky Equation with a Linearly Growing Mode in Each Direction
Journal of nonlinear science, v 31(6)
2021
Abstract
We consider the Kuramoto–Sivashinsky equation in two space dimensions. We establish the first proof of global existence of solutions in the presence of a linearly growing mode in both spatial directions for sufficiently small data. We develop a new method to this end, categorizing wavenumbers as low (linearly growing modes), intermediate (linearly decaying modes that serve as energy sinks for the low modes), and high (strongly linearly decaying modes). The low and intermediate modes are controlled by means of a Lyapunov function, while the high modes are controlled with operator estimates in function spaces based on the Wiener algebra.
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Details
- Title
- Global Solutions of the Two-Dimensional Kuramoto–Sivashinsky Equation with a Linearly Growing Mode in Each Direction
- Creators
- David M. Ambrose - Drexel UniversityAnna L. Mazzucato - Pennsylvania State University
- Publication Details
- Journal of nonlinear science, v 31(6)
- Publisher
- Springer US
- Grant note
- DMS-1907684; DMS-1909103 / National Science Foundation (US)
- Resource Type
- Journal article
- Language
- English
- Academic Unit
- Mathematics
- Web of Science ID
- WOS:000702674500001
- Scopus ID
- 2-s2.0-85116242206
- Other Identifier
- 991019168539404721
InCites Highlights
Data related to this publication, from InCites Benchmarking & Analytics tool:
- Collaboration types
- Domestic collaboration
- Web of Science research areas
- Mathematics, Applied
- Mechanics
- Physics, Mathematical