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Non-degeneracy, Mean Field Equations and the Onsager Theory of 2D Turbulence
Bartolucci, Daniele1; Jevnikar, Aleks1; Lee, Youngae2; Yang, Wen3
2018-10-01
Source PublicationARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS
ISSN0003-9527
Volume230Issue:1Pages:397-426
SubtypeArticle
AbstractThe understanding of some large energy, negative specific heat states in the Onsager description of 2D turbulence seem to require the analysis of a subtle open problem about bubbling solutions of the mean field equation. Motivated by this application we prove that, under suitable non-degeneracy assumptions on the associated m-vortex Hamiltonian, the m-point bubbling solutions of the mean field equation are non-degenerate as well. Then we deduce that the Onsager mean field equilibrium entropy is smooth and strictly convex in the high energy regime on domains of second kind.
WOS HeadingsScience & Technology ; Physical Sciences ; Technology
Funding OrganizationFIRB ; FIRB ; PRIN(2012, ERC PE1_11) ; PRIN(2012, ERC PE1_11) ; Consolidate the Foundations project 2015(ERC PE1_11) ; Consolidate the Foundations project 2015(ERC PE1_11) ; Univ. of Rome "Tor Vergata" ; Univ. of Rome "Tor Vergata" ; CAS Pioneer Hundred Talents Program ; CAS Pioneer Hundred Talents Program ; FIRB ; FIRB ; PRIN(2012, ERC PE1_11) ; PRIN(2012, ERC PE1_11) ; Consolidate the Foundations project 2015(ERC PE1_11) ; Consolidate the Foundations project 2015(ERC PE1_11) ; Univ. of Rome "Tor Vergata" ; Univ. of Rome "Tor Vergata" ; CAS Pioneer Hundred Talents Program ; CAS Pioneer Hundred Talents Program ; FIRB ; FIRB ; PRIN(2012, ERC PE1_11) ; PRIN(2012, ERC PE1_11) ; Consolidate the Foundations project 2015(ERC PE1_11) ; Consolidate the Foundations project 2015(ERC PE1_11) ; Univ. of Rome "Tor Vergata" ; Univ. of Rome "Tor Vergata" ; CAS Pioneer Hundred Talents Program ; CAS Pioneer Hundred Talents Program ; FIRB ; FIRB ; PRIN(2012, ERC PE1_11) ; PRIN(2012, ERC PE1_11) ; Consolidate the Foundations project 2015(ERC PE1_11) ; Consolidate the Foundations project 2015(ERC PE1_11) ; Univ. of Rome "Tor Vergata" ; Univ. of Rome "Tor Vergata" ; CAS Pioneer Hundred Talents Program ; CAS Pioneer Hundred Talents Program
DOI10.1007/s00205-018-1248-y
WOS KeywordLIOUVILLE-TYPE EQUATIONS ; STATISTICAL-MECHANICS DESCRIPTION ; 2-DIMENSIONAL EULER EQUATIONS ; ELLIPTIC EQUATION ; STATIONARY FLOWS ; RIEMANN SURFACES ; SINGULAR LIMITS ; UP SOLUTIONS ; BLOW ; DIMENSIONS
Indexed BySCI
Language英语
Funding OrganizationFIRB ; FIRB ; PRIN(2012, ERC PE1_11) ; PRIN(2012, ERC PE1_11) ; Consolidate the Foundations project 2015(ERC PE1_11) ; Consolidate the Foundations project 2015(ERC PE1_11) ; Univ. of Rome "Tor Vergata" ; Univ. of Rome "Tor Vergata" ; CAS Pioneer Hundred Talents Program ; CAS Pioneer Hundred Talents Program ; FIRB ; FIRB ; PRIN(2012, ERC PE1_11) ; PRIN(2012, ERC PE1_11) ; Consolidate the Foundations project 2015(ERC PE1_11) ; Consolidate the Foundations project 2015(ERC PE1_11) ; Univ. of Rome "Tor Vergata" ; Univ. of Rome "Tor Vergata" ; CAS Pioneer Hundred Talents Program ; CAS Pioneer Hundred Talents Program ; FIRB ; FIRB ; PRIN(2012, ERC PE1_11) ; PRIN(2012, ERC PE1_11) ; Consolidate the Foundations project 2015(ERC PE1_11) ; Consolidate the Foundations project 2015(ERC PE1_11) ; Univ. of Rome "Tor Vergata" ; Univ. of Rome "Tor Vergata" ; CAS Pioneer Hundred Talents Program ; CAS Pioneer Hundred Talents Program ; FIRB ; FIRB ; PRIN(2012, ERC PE1_11) ; PRIN(2012, ERC PE1_11) ; Consolidate the Foundations project 2015(ERC PE1_11) ; Consolidate the Foundations project 2015(ERC PE1_11) ; Univ. of Rome "Tor Vergata" ; Univ. of Rome "Tor Vergata" ; CAS Pioneer Hundred Talents Program ; CAS Pioneer Hundred Talents Program
WOS Research AreaMathematics ; Mechanics
WOS SubjectMathematics, Applied ; Mechanics
WOS IDWOS:000440977800010
PublisherSPRINGER
Citation statistics
Cited Times:6[WOS]   [WOS Record]     [Related Records in WOS]
Document Type期刊论文
Identifierhttp://ir.wipm.ac.cn/handle/112942/13027
Collection中国科学院武汉物理与数学研究所
Corresponding AuthorBartolucci, Daniele
Affiliation1.Univ Roma Tor Vergata, Dept Math, Via Ric Sci 1, I-00133 Rome, Italy
2.Kyungpook Natl Univ, Dept Math Educ, Teachers Coll, Daegu, South Korea
3.Chinese Acad Sci, Wuhan Inst Phys & Math, POB 71010, Wuhan 430071, Hubei, Peoples R China
Recommended Citation
GB/T 7714
Bartolucci, Daniele,Jevnikar, Aleks,Lee, Youngae,et al. Non-degeneracy, Mean Field Equations and the Onsager Theory of 2D Turbulence[J]. ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS,2018,230(1):397-426.
APA Bartolucci, Daniele,Jevnikar, Aleks,Lee, Youngae,&Yang, Wen.(2018).Non-degeneracy, Mean Field Equations and the Onsager Theory of 2D Turbulence.ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS,230(1),397-426.
MLA Bartolucci, Daniele,et al."Non-degeneracy, Mean Field Equations and the Onsager Theory of 2D Turbulence".ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS 230.1(2018):397-426.
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