Non-degeneracy, Mean Field Equations and the Onsager Theory of 2D Turbulence

doi:10.1007/s00205-018-1248-y

	Non-degeneracy, Mean Field Equations and the Onsager Theory of 2D Turbulence
	Bartolucci, Daniele 2; Jevnikar, Aleks 2; Lee, Youngae 1; Yang, Wen 3
刊名	ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS
	2018-10-01
卷号	230 期号:1 页码:397-426
ISSN号	0003-9527
DOI	10.1007/s00205-018-1248-y
文献子类	Article
英文摘要	The 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关键词	LIOUVILLE-TYPE EQUATIONS ; STATISTICAL-MECHANICS DESCRIPTION ; 2-DIMENSIONAL EULER EQUATIONS ; ELLIPTIC EQUATION ; STATIONARY FLOWS ; RIEMANN SURFACES ; SINGULAR LIMITS ; UP SOLUTIONS ; BLOW ; DIMENSIONS
WOS研究方向	Mathematics ; Mechanics
语种	英语
出版者	SPRINGER
WOS记录号	WOS:000440977800010
资助机构	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 ; 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
内容类型	期刊论文
源URL	[http://ir.wipm.ac.cn/handle/112942/13026]
专题	中国科学院武汉物理与数学研究所
通讯作者	Bartolucci, Daniele
作者单位	1.Kyungpook Natl Univ, Dept Math Educ, Teachers Coll, Daegu, South Korea 2.Univ Roma Tor Vergata, Dept Math, Via Ric Sci 1, I-00133 Rome, Italy 3.Chinese Acad Sci, Wuhan Inst Phys & Math, POB 71010, Wuhan 430071, Hubei, Peoples R China
推荐引用方式 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.