{"title":"Global in Time Weak Solutions to Singular Three-Dimensional Quasi-Geostrophic Systems","authors":"Yiran Hu","doi":"10.1137/23m1552917","DOIUrl":null,"url":null,"abstract":"SIAM Journal on Mathematical Analysis, Volume 56, Issue 5, Page 5881-5914, October 2024. <br/> Abstract. Geophysicists have studied three-dimensional quasi-geostrophic systems extensively. These systems describe stratified flows in the atmosphere on a large timescale and are widely used for forecasting atmospheric circulation. They couple an inviscid transport equation in [math] with an equation on the boundary satisfied by the trace, where [math] is either a two-dimensional torus or a bounded convex domain in [math]. In this paper, we show the existence of global in time weak solutions to a family of singular three-dimensional quasi-geostrophic systems with Ekman pumping, where the background density profile degenerates at the boundary. The proof is based on the construction of approximated models which combine the Galerkin method at the boundary and regularization processes in the bulk of the domain. The main difficulty is handling the degeneration of the background density profile at the boundary.","PeriodicalId":51150,"journal":{"name":"SIAM Journal on Mathematical Analysis","volume":null,"pages":null},"PeriodicalIF":2.2000,"publicationDate":"2024-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"SIAM Journal on Mathematical Analysis","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1137/23m1552917","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
SIAM Journal on Mathematical Analysis, Volume 56, Issue 5, Page 5881-5914, October 2024. Abstract. Geophysicists have studied three-dimensional quasi-geostrophic systems extensively. These systems describe stratified flows in the atmosphere on a large timescale and are widely used for forecasting atmospheric circulation. They couple an inviscid transport equation in [math] with an equation on the boundary satisfied by the trace, where [math] is either a two-dimensional torus or a bounded convex domain in [math]. In this paper, we show the existence of global in time weak solutions to a family of singular three-dimensional quasi-geostrophic systems with Ekman pumping, where the background density profile degenerates at the boundary. The proof is based on the construction of approximated models which combine the Galerkin method at the boundary and regularization processes in the bulk of the domain. The main difficulty is handling the degeneration of the background density profile at the boundary.
期刊介绍：
SIAM Journal on Mathematical Analysis (SIMA) features research articles of the highest quality employing innovative analytical techniques to treat problems in the natural sciences. Every paper has content that is primarily analytical and that employs mathematical methods in such areas as partial differential equations, the calculus of variations, functional analysis, approximation theory, harmonic or wavelet analysis, or dynamical systems. Additionally, every paper relates to a model for natural phenomena in such areas as fluid mechanics, materials science, quantum mechanics, biology, mathematical physics, or to the computational analysis of such phenomena.
Submission of a manuscript to a SIAM journal is representation by the author that the manuscript has not been published or submitted simultaneously for publication elsewhere.
Typical papers for SIMA do not exceed 35 journal pages. Substantial deviations from this page limit require that the referees, editor, and editor-in-chief be convinced that the increased length is both required by the subject matter and justified by the quality of the paper.
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