CSpace
Analysis of an inviscid zero-Mach number system in endpoint Besov spaces for finite-energy initial data
Fanelli, Francesco1; Liao, Xian2
2015-11-15
Source PublicationJOURNAL OF DIFFERENTIAL EQUATIONS
ISSN0022-0396
Volume259Issue:10Pages:5074-5114
AbstractThe present paper is the continuation of work [18], devoted to the study of an inviscid zero-Mach number system in the framework of endpoint Besov spaces of type B-infinity(1) (R-d), r is an element of [1, infinity], d > 2, which can be embedded in the Lipschitz class CO31. In particular, the largest case B-infinity,1(1) and the case of Holder spaces C-1,C-alpha are taken into account. The local in time well-posedness of this system is proved, under an additional finite-energy hypothesis on the initial data. The key to get this result is new a priori estimates for parabolic equations with variable coefficients in endpoint spaces B-infinity,r(s) (R-d), which are of independent interest. In the special case of space dimension d =2, we are able to give a lower bound for the lifespan, such that the solutions tend to be globally defined when the initial inhomogeneity is small. There, we will show refined a priori estimates in endpoint Besov spaces for transport equations. (C) 2015 Elsevier Inc. All rights reserved.
KeywordZero-Mach number system Endpoint Besov spaces Well-posedness Lifespan Parabolic equations Transport equations
DOI10.1016/j.jde.2015.06.038
Language英语
Funding ProjectMICINN, Spain[MTM2011-29306-C02-00] ; ERC Advanced Grant[FP7-246775 NUMERIWAVES] ; ESF Research Networking Programme OPT-PDE ; Basque Government[PI2010-04] ; project "Instabilities in Hydrodynamics" - Paris city hall (program "Emergences") ; Fondation Sciences Mathematiques de Paris ; China Scholarship Council ; Ministry of Education, Youth and Sports of the Czech Republic[ERC-CZ LL1202 MORE] ; MCM
WOS Research AreaMathematics
WOS SubjectMathematics
WOS IDWOS:000360258000005
PublisherACADEMIC PRESS INC ELSEVIER SCIENCE
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Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/20629
Collection中国科学院数学与系统科学研究院
Corresponding AuthorLiao, Xian
Affiliation1.Univ Paris Diderot, UMR 7586, Inst Math Jussieu Paris Rive Gauche, F-75205 Paris 13, France
2.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100864, Peoples R China
Recommended Citation
GB/T 7714
Fanelli, Francesco,Liao, Xian. Analysis of an inviscid zero-Mach number system in endpoint Besov spaces for finite-energy initial data[J]. JOURNAL OF DIFFERENTIAL EQUATIONS,2015,259(10):5074-5114.
APA Fanelli, Francesco,&Liao, Xian.(2015).Analysis of an inviscid zero-Mach number system in endpoint Besov spaces for finite-energy initial data.JOURNAL OF DIFFERENTIAL EQUATIONS,259(10),5074-5114.
MLA Fanelli, Francesco,et al."Analysis of an inviscid zero-Mach number system in endpoint Besov spaces for finite-energy initial data".JOURNAL OF DIFFERENTIAL EQUATIONS 259.10(2015):5074-5114.
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