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Existence of smooth solutions for the compressible barotropic Navier-Stokes-Korteweg system without increasing pressure law
Huang, Feimin1; Hong, Hakho2; Shi, Xiaoding3
2020-01-30
Source PublicationMATHEMATICAL METHODS IN THE APPLIED SCIENCES
ISSN0170-4214
Pages24
AbstractThis paper is concerned with a barotropic model of capillary compressible fluids describing the dynamics of a liquid-vapor mixture with diffuse interphase, in the case of general pressure law including Van der Waals gas. In the Sobolev spaces as close as possible to the physical energy spaces, we first prove local in time existence and uniqueness of the smooth solutions to the Cauchy problem in Rd(d=2,3), based on the estimates of a linearized system and the contraction mapping principle. Next, we show that there exists a global unique solution for the initial boundary value problem with periodic conditions in torus Td(d=2,3), by using a continuation argument of local solution. Notice that it is one of the main difficulties that pressure p is not increasing function of density rho.
Keywordcompressible Navier-Stokes-Korteweg system existence uniqueness Van der Waals gas
DOI10.1002/mma.6252
Indexed BySCI
Language英语
Funding ProjectNational Center forMathematics and Interdisciplinary Sciences, AMSS, CAS ; NSFC[11371349] ; National Natural Sciences Foundation of China[11671027] ; National Natural Sciences Foundation of China[11471321]
WOS Research AreaMathematics
WOS SubjectMathematics, Applied
WOS IDWOS:000510137100001
PublisherWILEY
Citation statistics
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/50799
Collection应用数学研究所
Corresponding AuthorHong, Hakho
Affiliation1.Chinese Acad Sci, Inst Appl Math, AMSS, Beijing, Peoples R China
2.State Acad Sci, Inst Math, Pyongyang, North Korea
3.Beijing Univ Chem Technol, Sch Sci, Dept Math, Beijing, Peoples R China
Recommended Citation
GB/T 7714
Huang, Feimin,Hong, Hakho,Shi, Xiaoding. Existence of smooth solutions for the compressible barotropic Navier-Stokes-Korteweg system without increasing pressure law[J]. MATHEMATICAL METHODS IN THE APPLIED SCIENCES,2020:24.
APA Huang, Feimin,Hong, Hakho,&Shi, Xiaoding.(2020).Existence of smooth solutions for the compressible barotropic Navier-Stokes-Korteweg system without increasing pressure law.MATHEMATICAL METHODS IN THE APPLIED SCIENCES,24.
MLA Huang, Feimin,et al."Existence of smooth solutions for the compressible barotropic Navier-Stokes-Korteweg system without increasing pressure law".MATHEMATICAL METHODS IN THE APPLIED SCIENCES (2020):24.
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