{"title":"Weak martingale solution of stochastic critical Oldroyd-B type models perturbed by pure jump noise","authors":"U. Manna, D. Mukherjee","doi":"10.1080/07362994.2021.1947855","DOIUrl":null,"url":null,"abstract":"Abstract We investigate the existence of a weak martingale solution for a two-dimensional critical viscoelastic flow of the Oldroyd type driven by pure jump Lévy noise. Due to the viscoelastic nature, noise in the equation modeling stress tensor is considered in the Marcus canonical form. Owing to the lack of dissipation and taking into account of the structure of the non-linear terms, the proof requires higher order estimates.","PeriodicalId":49474,"journal":{"name":"Stochastic Analysis and Applications","volume":"40 1","pages":"657 - 690"},"PeriodicalIF":0.8000,"publicationDate":"2021-08-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Stochastic Analysis and Applications","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1080/07362994.2021.1947855","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
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Abstract
Abstract We investigate the existence of a weak martingale solution for a two-dimensional critical viscoelastic flow of the Oldroyd type driven by pure jump Lévy noise. Due to the viscoelastic nature, noise in the equation modeling stress tensor is considered in the Marcus canonical form. Owing to the lack of dissipation and taking into account of the structure of the non-linear terms, the proof requires higher order estimates.
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Stochastic Analysis and Applications presents the latest innovations in the field of stochastic theory and its practical applications, as well as the full range of related approaches to analyzing systems under random excitation. In addition, it is the only publication that offers the broad, detailed coverage necessary for the interfield and intrafield fertilization of new concepts and ideas, providing the scientific community with a unique and highly useful service.
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