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Journal article
Global Existence and Analyticity for the 2D Kuramoto–Sivashinsky Equation
Journal of dynamics and differential equations, v 31(3), pp 1525-1547
01 Sep 2019
Abstract
There is little analytical theory for the behavior of solutions of the Kuramoto–Sivashinsky equation in two spatial dimensions over long times. We study the case in which the spatial domain is a two-dimensional torus. In this case, the linearized behavior depends on the size of the torus—in particular, for different sizes of the domain, there are different numbers of linearly growing modes. We prove that small solutions exist for all time if there are no linearly growing modes, proving also in this case that the radius of analyticity of solutions grows linearly in time. In the general case (i.e., in the presence of a finite number of growing modes), we make estimates for how the radius of analyticity of solutions changes in time.
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Details
- Title
- Global Existence and Analyticity for the 2D Kuramoto–Sivashinsky Equation
- Creators
- David M. Ambrose - Drexel UniversityAnna L. Mazzucato - Pennsylvania State University
- Publication Details
- Journal of dynamics and differential equations, v 31(3), pp 1525-1547
- Publisher
- Springer US
- Grant note
- 1515849; 1615457 / Division of Mathematical Sciences (http://dx.doi.org/10.13039/100000121)
- Resource Type
- Journal article
- Language
- English
- Academic Unit
- Mathematics
- Web of Science ID
- WOS:000482091300020
- Scopus ID
- 2-s2.0-85044482845
- Other Identifier
- 991019168222804721
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- Collaboration types
- Domestic collaboration
- Web of Science research areas
- Mathematics
- Mathematics, Applied