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Local existence of analytic sharp fronts for singular SQG
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Khor, Calvin and Rodrigo Diez, José L. (2021) Local existence of analytic sharp fronts for singular SQG. Nonlinear Analysis, 202 . 112116. doi:10.1016/j.na.2020.112116
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WRAP-local-existence-analytic-sharp-fronts-singular-SQG-Rodrigo-2021.pdf - Accepted Version - Requires a PDF viewer. Available under License Creative Commons Attribution Non-commercial No Derivatives 4.0. Download (855Kb) | Preview |
Official URL: https://doi.org/10.1016/j.na.2020.112116
Abstract
In this paper, we prove local existence and uniqueness of analytic sharp-front solutions to a generalised SQG equation by the use of an abstract Cauchy–Kovalevskaya theorem. Here, the velocity is determined by $u=|nabla|^{-2beta} nabla^{perp} \theta$ which (for $1<beta \leq 2$ ) is more singular than in SQG. This is achieved despite the appearance of pseudodifferential operators of order higher than one in our equation, by recasting our equation in a suitable integral form. We also provide a full proof of the abstract version of the Cauchy–Kovalevskaya theorem we use.
| Item Type: | Journal Article | ||||||||
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| Subjects: | Q Science > QA Mathematics | ||||||||
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||||
| Library of Congress Subject Headings (LCSH): | Geostrophic currents -- Mathematical models | ||||||||
| Journal or Publication Title: | Nonlinear Analysis | ||||||||
| Publisher: | Elsevier | ||||||||
| Official Date: | January 2021 | ||||||||
| Dates: |
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| Volume: | 202 | ||||||||
| Article Number: | 112116 | ||||||||
| DOI: | 10.1016/j.na.2020.112116 | ||||||||
| Status: | Peer Reviewed | ||||||||
| Publication Status: | Published | ||||||||
| Access rights to Published version: | Restricted or Subscription Access | ||||||||
| Date of first compliant deposit: | 11 January 2021 | ||||||||
| Date of first compliant Open Access: | 24 September 2021 | ||||||||
| RIOXX Funder/Project Grant: |
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