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Annales De L Institut Henri Poincare-Analyse Non Lineaire最新文献

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Generation of vortices in the Ginzburg–Landau heat flow 金兹堡-朗道热流涡旋的产生
IF 1.9 1区 数学
Annales De L Institut Henri Poincare-Analyse Non Lineaire Pub Date : 2022-11-28 DOI: 10.4171/aihpc/96
M. Kowalczyk, X. Lamy
{"title":"Generation of vortices in the Ginzburg–Landau heat flow","authors":"M. Kowalczyk, X. Lamy","doi":"10.4171/aihpc/96","DOIUrl":"https://doi.org/10.4171/aihpc/96","url":null,"abstract":"We consider the Ginzburg-Landau heat flow on the two-dimensional flat torus, starting from an initial data with a finite number of nondegenerate zeros -- but possibly very high initial energy. We show that the initial zeros are conserved and the flow rapidly enters a logarithmic energy regime, from which the evolution of vortices can be described by the works of Bethuel, Orlandi and Smets.","PeriodicalId":55514,"journal":{"name":"Annales De L Institut Henri Poincare-Analyse Non Lineaire","volume":"15 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2022-11-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81916956","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Global and local energy minimizers for a nanowire growth model 纳米线生长模型的全局和局部能量最小化
IF 1.9 1区 数学
Annales De L Institut Henri Poincare-Analyse Non Lineaire Pub Date : 2022-11-04 DOI: 10.4171/aihpc/54
I. Fonseca, N. Fusco, G. Leoni, M. Morini
{"title":"Global and local energy minimizers for a nanowire growth model","authors":"I. Fonseca, N. Fusco, G. Leoni, M. Morini","doi":"10.4171/aihpc/54","DOIUrl":"https://doi.org/10.4171/aihpc/54","url":null,"abstract":"We consider a model for vapor-liquid-solid growth of nanowires proposed in the physical literature. Liquid drops are described as local or global volume-constrained minimizers of the capillarity energy outside a semi-infinite convex obstacle modeling the nanowire. We first address the existence of global minimizers and then, in the case of rotationally symmetric nanowires, we investigate how the presence of a sharp edge affects the shape of local minimizers and the validity of Young’s law. π 2 > θ λ , and max { π 2 , θ λ } < θ < π . In the first two cases, we show that S θ is a strict local minimizer. For a precise formulation we refer to the statements of Theorems 4.4 and 4.8 below. The case max { π 2 , θ λ } < θ < π is more delicate, and we are only able to show strict local minimimality of S θ with respect to admissible sets that coincide with S θ in a neighborhood of the north pole (see Theorem 4.9). The proofs of these theorems rely on calibration techniques and on the construction of foliating families of rotationally symmetric surfaces with constant mean curvature.","PeriodicalId":55514,"journal":{"name":"Annales De L Institut Henri Poincare-Analyse Non Lineaire","volume":"77 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2022-11-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77475217","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 3
Dynamics of nonlinear Klein–Gordon equations in low regularity on $mathbb{S}^2$ $mathbb{S}^2$上低正则性非线性Klein-Gordon方程的动力学
IF 1.9 1区 数学
Annales De L Institut Henri Poincare-Analyse Non Lineaire Pub Date : 2022-11-04 DOI: 10.4171/aihpc/55
J. Bernier, B. Grébert, Gabriel Rivière
{"title":"Dynamics of nonlinear Klein–Gordon equations in low regularity on $mathbb{S}^2$","authors":"J. Bernier, B. Grébert, Gabriel Rivière","doi":"10.4171/aihpc/55","DOIUrl":"https://doi.org/10.4171/aihpc/55","url":null,"abstract":"","PeriodicalId":55514,"journal":{"name":"Annales De L Institut Henri Poincare-Analyse Non Lineaire","volume":"99 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2022-11-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85807460","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Fine multibubble analysis in the higher-dimensional Brezis–Nirenberg problem 高维Brezis-Nirenberg问题的精细多泡分析
IF 1.9 1区 数学
Annales De L Institut Henri Poincare-Analyse Non Lineaire Pub Date : 2022-11-01 DOI: 10.4171/aihpc/95
Tobias König, P. Laurain
{"title":"Fine multibubble analysis in the higher-dimensional Brezis–Nirenberg problem","authors":"Tobias König, P. Laurain","doi":"10.4171/aihpc/95","DOIUrl":"https://doi.org/10.4171/aihpc/95","url":null,"abstract":"For a bounded set $Omega subset mathbb R^N$ and a perturbation $V in C^1(overline{Omega})$, we analyze the concentration behavior of a blow-up sequence of positive solutions to [ -Delta u_epsilon + epsilon V = N(N-2) u_epsilon^frac{N+2}{N-2} ] for dimensions $N geq 4$, which are non-critical in the sense of the Brezis--Nirenberg problem. For the general case of multiple concentration points, we prove that concentration points are isolated and characterize the vector of these points as a critical point of a suitable function derived from the Green's function of $-Delta$ on $Omega$. Moreover, we give the leading order expression of the concentration speed. This paper, with a recent one by the authors (arXiv:2208.12337) in dimension $N = 3$, gives a complete picture of blow-up phenomena in the Brezis-Nirenberg framework.","PeriodicalId":55514,"journal":{"name":"Annales De L Institut Henri Poincare-Analyse Non Lineaire","volume":"69 7 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2022-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91106448","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
Erratum to “On minimal laminations of the torus” “关于环面最小层积”的勘误
IF 1.9 1区 数学
Annales De L Institut Henri Poincare-Analyse Non Lineaire Pub Date : 2022-10-18 DOI: 10.4171/aihpc/60
V. Bangert
{"title":"Erratum to “On minimal laminations of the torus”","authors":"V. Bangert","doi":"10.4171/aihpc/60","DOIUrl":"https://doi.org/10.4171/aihpc/60","url":null,"abstract":"","PeriodicalId":55514,"journal":{"name":"Annales De L Institut Henri Poincare-Analyse Non Lineaire","volume":"25 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2022-10-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72529686","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A quantitative strong parabolic maximum principle and application to a taxis-type migration–consumption model involving signal-dependent degenerate diffusion 一个定量强抛物极大值原理及其在包含信号依赖退化扩散的出租车型迁移-消耗模型中的应用
IF 1.9 1区 数学
Annales De L Institut Henri Poincare-Analyse Non Lineaire Pub Date : 2022-09-26 DOI: 10.4171/aihpc/73
M. Winkler
{"title":"A quantitative strong parabolic maximum principle and application to a taxis-type migration–consumption model involving signal-dependent degenerate diffusion","authors":"M. Winkler","doi":"10.4171/aihpc/73","DOIUrl":"https://doi.org/10.4171/aihpc/73","url":null,"abstract":"The taxis-type migration-consumption model accounting for signal-dependent motilities, as given by ( u t = ∆ ( ) is considered for suitably smooth functions φ : [0 , ∞ ) → R which are such that φ > 0 on (0 , ∞ ), but that in addition φ (0) = 0 with φ ′ (0) > 0. In order to appropriately cope with the diffusion degeneracies thereby included, this study separately examines the Neumann problem for the linear equation and establishes a statement on how pointwise positive lower bounds for nonnegative solutions depend on the supremum and the mass of the initial data, and on integrability features of a and b . This is thereafter used as a key tool in the derivation of a result on global existence of solutions to ( ⋆ ), smooth and classical for positive times, under the mere assumption that the suitably regular initial data be nonnegative in both components. Apart from that, these solutions are seen to stabilize toward some equilibrium, and as a qualitative effect genuinely due to degeneracy in diffusion, a criterion on initial smallness of the second component is identified as sufficient for this limit state to be spatially nonconstant.","PeriodicalId":55514,"journal":{"name":"Annales De L Institut Henri Poincare-Analyse Non Lineaire","volume":"3 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2022-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79369368","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 13
Estimation of non-uniqueness and short-time asymptotic expansions for Navier–Stokes flows Navier-Stokes流的非唯一性估计及短时渐近展开式
IF 1.9 1区 数学
Annales De L Institut Henri Poincare-Analyse Non Lineaire Pub Date : 2022-06-07 DOI: 10.4171/aihpc/92
Z. Bradshaw, P. Phelps
{"title":"Estimation of non-uniqueness and short-time asymptotic expansions for Navier–Stokes flows","authors":"Z. Bradshaw, P. Phelps","doi":"10.4171/aihpc/92","DOIUrl":"https://doi.org/10.4171/aihpc/92","url":null,"abstract":"There is considerable evidence that solutions to the non-forced 3D Navier-Stokes equations in the natural energy space are not unique. Assuming this is the case, it becomes important to quantify how non-uniqueness evolves. In this paper we provide an algebraic estimate for how rapidly two possibly non-unique solutions can separate over a compact spatial region in which the initial data has sub-critical regularity. Outside of this compact region, the data is only assumed to be in the scaling critical weak Lebesgue space and can be large. In order to establish this separation rate, we develop a new spatially local, short-time asymptotic expansion which is of independent interest.","PeriodicalId":55514,"journal":{"name":"Annales De L Institut Henri Poincare-Analyse Non Lineaire","volume":"208 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2022-06-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82520476","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Degenerate stability of some Sobolev inequalities 一些Sobolev不等式的退化稳定性
IF 1.9 1区 数学
Annales De L Institut Henri Poincare-Analyse Non Lineaire Pub Date : 2022-06-02 DOI: 10.4171/aihpc/35
R. Frank
{"title":"Degenerate stability of some Sobolev inequalities","authors":"R. Frank","doi":"10.4171/aihpc/35","DOIUrl":"https://doi.org/10.4171/aihpc/35","url":null,"abstract":"","PeriodicalId":55514,"journal":{"name":"Annales De L Institut Henri Poincare-Analyse Non Lineaire","volume":"43 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2022-06-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77519824","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Existence and weak–strong uniqueness for Maxwell–Stefan–Cahn–Hilliard systems Maxwell-Stefan-Cahn-Hilliard系统的存在性和弱-强唯一性
IF 1.9 1区 数学
Annales De L Institut Henri Poincare-Analyse Non Lineaire Pub Date : 2022-05-13 DOI: 10.4171/aihpc/89
Xiaokai Huo, A. Jungel, A. Tzavaras
{"title":"Existence and weak–strong uniqueness for Maxwell–Stefan–Cahn–Hilliard systems","authors":"Xiaokai Huo, A. Jungel, A. Tzavaras","doi":"10.4171/aihpc/89","DOIUrl":"https://doi.org/10.4171/aihpc/89","url":null,"abstract":"A Maxwell-Stefan system for fluid mixtures with driving forces depending on Cahn-Hilliard-type chemical potentials is analyzed. The corresponding parabolic cross-diffusion equations contain fourth-order derivatives and are considered in a bounded domain with no-flux boundary conditions. The main difficulty of the analysis is the degeneracy of the diffusion matrix, which is overcome by proving the positive definiteness of the matrix on a subspace and using the Bott--Duffin matrix inverse. The global existence of weak solutions and a weak-strong uniqueness property are shown by a careful combination of (relative) energy and entropy estimates, yielding $H^2(Omega)$ bounds for the densities, which cannot be obtained from the energy or entropy inequalities alone.","PeriodicalId":55514,"journal":{"name":"Annales De L Institut Henri Poincare-Analyse Non Lineaire","volume":"107 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2022-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91263517","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 3
On local energy decay for solutions of the Benjamin–Ono equation Benjamin-Ono方程解的局部能量衰减
IF 1.9 1区 数学
Annales De L Institut Henri Poincare-Analyse Non Lineaire Pub Date : 2022-04-27 DOI: 10.4171/aihpc/81
R. Freire, F. Linares, Claudio Muñoz, G. Ponce
{"title":"On local energy decay for solutions of the Benjamin–Ono equation","authors":"R. Freire, F. Linares, Claudio Muñoz, G. Ponce","doi":"10.4171/aihpc/81","DOIUrl":"https://doi.org/10.4171/aihpc/81","url":null,"abstract":"We consider the long time dynamics of large solutions to the Benjamin-Ono equation. Using virial techniques, we describe regions of space where every solution in a suitable Sobolev space must decay to zero along sequences of times. Moreover, in the case of exterior regions, we prove complete decay for any sequence of times. The remaining regions not treated here are essentially the strong dispersion and soliton regions.","PeriodicalId":55514,"journal":{"name":"Annales De L Institut Henri Poincare-Analyse Non Lineaire","volume":"22 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2022-04-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86365424","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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