{"title":"论流体力学的非线性随机分数微分方程","authors":"Marc Jornet , Juan J. Nieto","doi":"10.1016/j.physd.2024.134400","DOIUrl":null,"url":null,"abstract":"<div><div>We deal with a nonlinear stochastic fractional differential equation, in the Caputo and Itô senses, that generalizes important models of fluid dynamics, such as the Bagley–Torvik and the Basset equations. We investigate the integral formulation, existence, uniqueness, moment bounds, and continuity with respect to input data. Some conjectures are raised.</div></div>","PeriodicalId":2,"journal":{"name":"ACS Applied Bio Materials","volume":null,"pages":null},"PeriodicalIF":4.6000,"publicationDate":"2024-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On a nonlinear stochastic fractional differential equation of fluid dynamics\",\"authors\":\"Marc Jornet , Juan J. Nieto\",\"doi\":\"10.1016/j.physd.2024.134400\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>We deal with a nonlinear stochastic fractional differential equation, in the Caputo and Itô senses, that generalizes important models of fluid dynamics, such as the Bagley–Torvik and the Basset equations. We investigate the integral formulation, existence, uniqueness, moment bounds, and continuity with respect to input data. Some conjectures are raised.</div></div>\",\"PeriodicalId\":2,\"journal\":{\"name\":\"ACS Applied Bio Materials\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":4.6000,\"publicationDate\":\"2024-10-10\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"ACS Applied Bio Materials\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0167278924003506\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATERIALS SCIENCE, BIOMATERIALS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"ACS Applied Bio Materials","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0167278924003506","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATERIALS SCIENCE, BIOMATERIALS","Score":null,"Total":0}
On a nonlinear stochastic fractional differential equation of fluid dynamics
We deal with a nonlinear stochastic fractional differential equation, in the Caputo and Itô senses, that generalizes important models of fluid dynamics, such as the Bagley–Torvik and the Basset equations. We investigate the integral formulation, existence, uniqueness, moment bounds, and continuity with respect to input data. Some conjectures are raised.