We investigate the global existence of smooth solutions to the three dimensional generalized Hall-MHD system with mixed partial viscosity in this work. The diffusion of mixed partial viscosity is weaker than that of full viscosity, which cases new difficulty in proving global smooth solutions. Moreover, Hall term heightens the level of nonlinearity of the standard MHD system. Global smooth solutions are established by using energy method and the bootstrapping argument, provided that the initial data is enough small. AMS Subject Classifications: 76D03, 76W05 Chinese Library Classifications: O175.29
{"title":"Global Existence of Smooth Solutions to Three Dimensional Hall-MHD System with Mixed Partial Viscosity","authors":"Yuzhu Wang","doi":"10.4208/jpde.v34.n1.1","DOIUrl":"https://doi.org/10.4208/jpde.v34.n1.1","url":null,"abstract":"We investigate the global existence of smooth solutions to the three dimensional generalized Hall-MHD system with mixed partial viscosity in this work. The diffusion of mixed partial viscosity is weaker than that of full viscosity, which cases new difficulty in proving global smooth solutions. Moreover, Hall term heightens the level of nonlinearity of the standard MHD system. Global smooth solutions are established by using energy method and the bootstrapping argument, provided that the initial data is enough small. AMS Subject Classifications: 76D03, 76W05 Chinese Library Classifications: O175.29","PeriodicalId":43504,"journal":{"name":"Journal of Partial Differential Equations","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2021-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88467956","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"New Class of Kirchhoff Type Equations with Kelvin-Voigt Damping and General Nonlinearity: Local Existence and Blow-up in Solutions","authors":"HanniDridi & KhaledZennir","doi":"10.4208/jpde.v34.n4.2","DOIUrl":"https://doi.org/10.4208/jpde.v34.n4.2","url":null,"abstract":"","PeriodicalId":43504,"journal":{"name":"Journal of Partial Differential Equations","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2021-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76419317","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Adaptive Segmentation Model for Images with Intensity Inhomogeneity based on Local Neighborhood Contrast","authors":"global XuyuanZhang","doi":"10.4208/jpde.v34.n3.2","DOIUrl":"https://doi.org/10.4208/jpde.v34.n3.2","url":null,"abstract":"","PeriodicalId":43504,"journal":{"name":"Journal of Partial Differential Equations","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2021-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76941175","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Trudinger-Moser Type Inequality Under Lorentz-Sobolev Norms Constraint","authors":"Zhu Yifeng","doi":"10.4208/JPDE.V34.N2.2","DOIUrl":"https://doi.org/10.4208/JPDE.V34.N2.2","url":null,"abstract":"","PeriodicalId":43504,"journal":{"name":"Journal of Partial Differential Equations","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2021-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77813155","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"The Nonexistence of the Solutions for the Non-Newtonian Filtration Equation with Absorption","authors":"global QitongOu","doi":"10.4208/jpde.v34.n4.4","DOIUrl":"https://doi.org/10.4208/jpde.v34.n4.4","url":null,"abstract":"","PeriodicalId":43504,"journal":{"name":"Journal of Partial Differential Equations","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2021-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80338951","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Finite-Time Blow-Up and Local Existence for Chemotaxis System with a General Memory Term","authors":"global YingdongWu","doi":"10.4208/jpde.v34.n1.5","DOIUrl":"https://doi.org/10.4208/jpde.v34.n1.5","url":null,"abstract":"","PeriodicalId":43504,"journal":{"name":"Journal of Partial Differential Equations","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2021-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86244894","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Quenching Time Estimates for Semilinear Parabolic Equations Controlled by Two Absorption Sources in Control System","authors":"global sci","doi":"10.4208/jpde.v33.n1.3","DOIUrl":"https://doi.org/10.4208/jpde.v33.n1.3","url":null,"abstract":"","PeriodicalId":43504,"journal":{"name":"Journal of Partial Differential Equations","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2020-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75644094","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
. In this paper we study the local or global (in time) existence of small data solutions to semi-linear fractional σ − evolution equations with nonlinear memory. Our main goals is to explain on the one hand the influence of the memory term and on the other hand the influence of higher regularity of the data on qualitative properties of solutions.
{"title":"Semi-Linear Fractional σ-Evolution Equations with Nonlinear Memory","authors":"A. K. Mezadek","doi":"10.4208/jpde.v33.n4.1","DOIUrl":"https://doi.org/10.4208/jpde.v33.n4.1","url":null,"abstract":". In this paper we study the local or global (in time) existence of small data solutions to semi-linear fractional σ − evolution equations with nonlinear memory. Our main goals is to explain on the one hand the influence of the memory term and on the other hand the influence of higher regularity of the data on qualitative properties of solutions.","PeriodicalId":43504,"journal":{"name":"Journal of Partial Differential Equations","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2020-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75029405","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Gradient Estimates for a Nonlinear Heat Equation Under Finsler-geometric Flow","authors":"global sci","doi":"10.4208/jpde.v33.n1.2","DOIUrl":"https://doi.org/10.4208/jpde.v33.n1.2","url":null,"abstract":"","PeriodicalId":43504,"journal":{"name":"Journal of Partial Differential Equations","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2020-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81805817","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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