{"title":"Euler–Lagrangian Approach to Stochastic Euler Equations in Sobolev Spaces","authors":"Christian Olivera, Juan D. Londoño","doi":"10.1007/s00021-023-00808-5","DOIUrl":null,"url":null,"abstract":"<div><p>The purpose of this paper is to establish the equivalence between Lagrangian and classical formulations for the stochastic incompressible Euler equations, the proof is based on Ito–Wentzell–Kunita formula and stochastic analysis techniques. Moreover, we prove a local existence result for the Lagrangian formulation in suitable Sobolev Spaces.\n</p></div>","PeriodicalId":649,"journal":{"name":"Journal of Mathematical Fluid Mechanics","volume":null,"pages":null},"PeriodicalIF":1.2000,"publicationDate":"2023-06-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Mathematical Fluid Mechanics","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s00021-023-00808-5","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
The purpose of this paper is to establish the equivalence between Lagrangian and classical formulations for the stochastic incompressible Euler equations, the proof is based on Ito–Wentzell–Kunita formula and stochastic analysis techniques. Moreover, we prove a local existence result for the Lagrangian formulation in suitable Sobolev Spaces.
期刊介绍：
The Journal of Mathematical Fluid Mechanics (JMFM)is a forum for the publication of high-quality peer-reviewed papers on the mathematical theory of fluid mechanics, with special regards to the Navier-Stokes equations. As an important part of that, the journal encourages papers dealing with mathematical aspects of computational theory, as well as with applications in science and engineering. The journal also publishes in related areas of mathematics that have a direct bearing on the mathematical theory of fluid mechanics. All papers will be characterized by originality and mathematical rigor. For a paper to be accepted, it is not enough that it contains original results. In fact, results should be highly relevant to the mathematical theory of fluid mechanics, and meet a wide readership.
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