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On the spectral characterization of Besse and Zoll Reeb flows Besse和Zoll Reeb流的谱特征
IF 1.9 1区 数学
Annales De L Institut Henri Poincare-Analyse Non Lineaire Pub Date : 2021-05-01 DOI: 10.1016/j.anihpc.2020.08.004
Viktor L. Ginzburg , Başak Z. Gürel , Marco Mazzucchelli
{"title":"On the spectral characterization of Besse and Zoll Reeb flows","authors":"Viktor L. Ginzburg ,&nbsp;Başak Z. Gürel ,&nbsp;Marco Mazzucchelli","doi":"10.1016/j.anihpc.2020.08.004","DOIUrl":"10.1016/j.anihpc.2020.08.004","url":null,"abstract":"<div><p><span><span>A closed contact manifold is called Besse when all its Reeb orbits are closed, and Zoll when they have the same minimal period. In this paper, we provide a characterization of Besse contact forms for convex contact spheres and Riemannian </span>unit tangent bundles in terms of </span><span><math><msup><mrow><mi>S</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span><span>-equivariant spectral invariants. Furthermore, for restricted contact type hypersurfaces of symplectic vector spaces, we give a sufficient condition for the Besse property via the Ekeland–Hofer capacities.</span></p></div>","PeriodicalId":55514,"journal":{"name":"Annales De L Institut Henri Poincare-Analyse Non Lineaire","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2021-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.anihpc.2020.08.004","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77041716","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: 9
Almost periodic invariant tori for the NLS on the circle 圆上NLS的几乎周期不变环面
IF 1.9 1区 数学
Annales De L Institut Henri Poincare-Analyse Non Lineaire Pub Date : 2021-05-01 DOI: 10.1016/j.anihpc.2020.09.003
Luca Biasco, Jessica Elisa Massetti, Michela Procesi
{"title":"Almost periodic invariant tori for the NLS on the circle","authors":"Luca Biasco,&nbsp;Jessica Elisa Massetti,&nbsp;Michela Procesi","doi":"10.1016/j.anihpc.2020.09.003","DOIUrl":"10.1016/j.anihpc.2020.09.003","url":null,"abstract":"<div><p><span>In this paper we study the existence and linear stability of almost periodic solutions for a NLS equation on the circle with external parameters. Starting from the seminal result of Bourgain in </span><span>[15]</span><span> on the quintic NLS, we propose a novel approach allowing to prove in a unified framework the persistence of finite and infinite dimensional invariant tori, which are the support of the desired solutions. The persistence result is given through a rather abstract “counter-term theorem” à la Herman, directly in the original elliptic variables without passing to action-angle ones. Our framework allows us to find “many more” almost periodic solutions with respect to the existing literature and consider also non-translation invariant PDEs.</span></p></div>","PeriodicalId":55514,"journal":{"name":"Annales De L Institut Henri Poincare-Analyse Non Lineaire","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2021-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.anihpc.2020.09.003","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81397197","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: 17
Some Liouville theorems for stationary Navier-Stokes equations in Lebesgue and Morrey spaces Lebesgue和Morrey空间中平稳Navier-Stokes方程的若干Liouville定理
IF 1.9 1区 数学
Annales De L Institut Henri Poincare-Analyse Non Lineaire Pub Date : 2021-05-01 DOI: 10.1016/j.anihpc.2020.08.006
Diego Chamorro , Oscar Jarrín , Pierre-Gilles Lemarié-Rieusset
{"title":"Some Liouville theorems for stationary Navier-Stokes equations in Lebesgue and Morrey spaces","authors":"Diego Chamorro ,&nbsp;Oscar Jarrín ,&nbsp;Pierre-Gilles Lemarié-Rieusset","doi":"10.1016/j.anihpc.2020.08.006","DOIUrl":"10.1016/j.anihpc.2020.08.006","url":null,"abstract":"<div><p>Uniqueness of Leray solutions of the 3D Navier-Stokes equations is a challenging open problem. In this article we will study this problem for the 3D stationary Navier-Stokes equations in the whole space <span><math><msup><mrow><mi>R</mi></mrow><mrow><mn>3</mn></mrow></msup></math></span><span>. Under some additional hypotheses, stated in terms of Lebesgue and Morrey spaces, we will show that the trivial solution </span><span><math><mover><mrow><mi>U</mi></mrow><mrow><mo>→</mo></mrow></mover><mo>=</mo><mn>0</mn></math></span><span><span> is the unique solution. This type of results are known as </span>Liouville theorems.</span></p></div>","PeriodicalId":55514,"journal":{"name":"Annales De L Institut Henri Poincare-Analyse Non Lineaire","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2021-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.anihpc.2020.08.006","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89439447","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: 39
The pressureless damped Euler–Riesz equations 无压阻尼欧拉-里兹方程
IF 1.9 1区 数学
Annales De L Institut Henri Poincare-Analyse Non Lineaire Pub Date : 2021-04-12 DOI: 10.4171/aihpc/48
Young-Pil Choi, Jinwook Jung
{"title":"The pressureless damped Euler–Riesz equations","authors":"Young-Pil Choi, Jinwook Jung","doi":"10.4171/aihpc/48","DOIUrl":"https://doi.org/10.4171/aihpc/48","url":null,"abstract":"In this paper, we analyze the pressureless damped Euler–Riesz equations posed in either R or T. We construct the global-in-time existence and uniqueness of classical solutions for the system around a constant background state. We also establish large-time behaviors of classical solutions showing the solutions towards the equilibrium as time goes to infinity. For the whole space case, we first show the algebraic decay rate of solutions under additional assumptions on the initial data compared to the existence theory. We then refine the argument to have the exponential decay rate of convergence even in the whole space. In the case of the periodic domain, without any further regularity assumptions on the initial data, we provide the exponential convergence of solutions.","PeriodicalId":55514,"journal":{"name":"Annales De L Institut Henri Poincare-Analyse Non Lineaire","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2021-04-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89430746","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
A variational approach to frozen planet orbits in helium 氦中冰冻行星轨道的变分方法
IF 1.9 1区 数学
Annales De L Institut Henri Poincare-Analyse Non Lineaire Pub Date : 2021-03-29 DOI: 10.4171/aihpc/46
K. Cieliebak, U. Frauenfelder, E. Volkov
{"title":"A variational approach to frozen planet orbits in helium","authors":"K. Cieliebak, U. Frauenfelder, E. Volkov","doi":"10.4171/aihpc/46","DOIUrl":"https://doi.org/10.4171/aihpc/46","url":null,"abstract":"We present variational characterizations of frozen planet orbits for the helium atom in the Lagrangian and the Hamiltonian picture. They are based on a Levi-Civita regularization with different time reparametrizations for the two electrons and lead to nonlocal functionals. Within this variational setup, we deform the helium problem to one where the two electrons interact only by their mean values and use this to deduce the existence of frozen planet orbits.","PeriodicalId":55514,"journal":{"name":"Annales De L Institut Henri Poincare-Analyse Non Lineaire","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2021-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80682225","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: 8
Unbounded growth of the energy density associated to the Schrödinger map and the binormal flow 能量密度的无界增长与Schrödinger图和双法线流相关
IF 1.9 1区 数学
Annales De L Institut Henri Poincare-Analyse Non Lineaire Pub Date : 2021-03-23 DOI: 10.4171/aihpc/24
V. Banica, L. Vega
{"title":"Unbounded growth of the energy density associated to the Schrödinger map and the binormal flow","authors":"V. Banica, L. Vega","doi":"10.4171/aihpc/24","DOIUrl":"https://doi.org/10.4171/aihpc/24","url":null,"abstract":"We consider the binormal flow equation, which is a model for the dynamics of vortex filaments in Euler equations. Geometrically it is a flow of curves in three dimensions, explicitly connected to the 1-D Schrödinger map with values on the 2-D sphere, and to the 1-D cubic Schrödinger equation. Although these equations are completely integrable we show the existence of an unbounded growth of the energy density. The density is given by the amplitude of the high frequencies of the derivative of the tangent vectors of the curves, thus giving information of the oscillation at small scales. In the setting of vortex filaments the variation of the tangent vectors is related to the derivative of the direction of the vorticity, that according to the Constantin-Fefferman-Majda criterion plays a relevant role in the possible development of singularities for Euler equations.","PeriodicalId":55514,"journal":{"name":"Annales De L Institut Henri Poincare-Analyse Non Lineaire","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2021-03-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82127656","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: 1
A mathematical analysis of the Kakinuma model for interfacial gravity waves. Part I: Structures and well-posedness 界面重力波的Kakinuma模型的数学分析。第一部分:结构和姿势
IF 1.9 1区 数学
Annales De L Institut Henri Poincare-Analyse Non Lineaire Pub Date : 2021-03-23 DOI: 10.4171/aihpc/82
V. Duchêne, T. Iguchi
{"title":"A mathematical analysis of the Kakinuma model for interfacial gravity waves. Part I: Structures and well-posedness","authors":"V. Duchêne, T. Iguchi","doi":"10.4171/aihpc/82","DOIUrl":"https://doi.org/10.4171/aihpc/82","url":null,"abstract":"We consider a model, which we named the Kakinuma model, for interfacial gravity waves. As is well-known, the full model for interfacial gravity waves has a variational structure whose Lagrangian is an extension of Luke's Lagrangian for surface gravity waves, that is, water waves. The Kakinuma model is a system of Euler-Lagrange equations for approximate Lagrangians, which are obtained by approximating the velocity potentials in the Lagrangian for the full model. In this paper, we first analyze the linear dispersion relation for the Kakinuma model and show that the dispersion curves highly fit that of the full model in the shallow water regime. We then analyze the linearized equations around constant states and derive a stability condition, which is satisfied for small initial data when the denser water is below the lighter water. We show that the initial value problem is in fact well-posed locally in time in Sobolev spaces under the stability condition, the non-cavitation assumption and intrinsic compatibility conditions in spite of the fact that the initial value problem for the full model does not have any stability domain so that its initial value problem is ill-posed in Sobolev spaces. Moreover, it is shown that the Kakinuma model enjoys a Hamiltonian structure and has conservative quantities: mass, total energy, and in the case of the flat bottom, momentum.","PeriodicalId":55514,"journal":{"name":"Annales De L Institut Henri Poincare-Analyse Non Lineaire","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2021-03-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82078960","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: 1
Interacting helical traveling waves for the Gross–Pitaevskii equation Gross-Pitaevskii方程的相互作用螺旋行波
IF 1.9 1区 数学
Annales De L Institut Henri Poincare-Analyse Non Lineaire Pub Date : 2021-03-19 DOI: 10.4171/aihpc/32
J. D'avila, M. Pino, María Medina, Rémy Rodiac
{"title":"Interacting helical traveling waves for the Gross–Pitaevskii equation","authors":"J. D'avila, M. Pino, María Medina, Rémy Rodiac","doi":"10.4171/aihpc/32","DOIUrl":"https://doi.org/10.4171/aihpc/32","url":null,"abstract":"Abstract. We consider the 3D Gross-Pitaevskii equation i∂tψ +∆ψ + (1 − |ψ| )ψ = 0 for ψ : R× R → C and construct traveling waves solutions to this equation. These are solutions of the form ψ(t, x) = u(x1, x2, x3 −Ct) with a velocity C of order ε| log ε| for a small parameter ε > 0. We build two different types of solutions. For the first type, the functions u have a zero-set (vortex set) close to an union of n helices for n ≥ 2 and near these helices u has degree 1. For the second type, the functions u have a vortex filament of degree −1 near the vertical axis e3 and n ≥ 4 vortex filaments of degree +1 near helices whose axis is e3. In both cases the helices are at a distance of order 1/(ε √","PeriodicalId":55514,"journal":{"name":"Annales De L Institut Henri Poincare-Analyse Non Lineaire","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2021-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72530786","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
Adaptation to a heterogeneous patchy environment with non-local dispersion 适应非局部分散的异质斑块环境
IF 1.9 1区 数学
Annales De L Institut Henri Poincare-Analyse Non Lineaire Pub Date : 2021-03-17 DOI: 10.4171/aihpc/59
Alexis L'eculier, S. Mirrahimi
{"title":"Adaptation to a heterogeneous patchy environment with non-local dispersion","authors":"Alexis L'eculier, S. Mirrahimi","doi":"10.4171/aihpc/59","DOIUrl":"https://doi.org/10.4171/aihpc/59","url":null,"abstract":"In this work, we provide an asymptotic analysis of the solutions to an elliptic integro-differential equation. This equation describes the evolutionary equilibria of a phenotypically structured population, subject to selection, mutation, and both local and non-local dispersion in a spatially heterogeneous, possibly patchy, environment. Considering small effects of mutations, we provide an asymptotic description of the equilibria of the phenotypic density. This asymptotic description involves a Hamilton-Jacobi equation with constraint coupled with an eigenvalue problem. Based on such analysis, we characterize some qualitative properties of the phenotypic density at equilibrium depending on the heterogeneity of the environment. In particular, we show that when the heterogeneity of the environment is low, the population concentrates around a single phenotypic trait leading to a unimodal phenotypic distribution. On the contrary, a strong fragmentation of the environment leads to multi-modal phenotypic distributions.","PeriodicalId":55514,"journal":{"name":"Annales De L Institut Henri Poincare-Analyse Non Lineaire","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2021-03-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85664127","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: 1
Nonnegative control of finite-dimensional linear systems 有限维线性系统的非负控制
IF 1.9 1区 数学
Annales De L Institut Henri Poincare-Analyse Non Lineaire Pub Date : 2021-03-01 DOI: 10.1016/j.anihpc.2020.07.004
Jérôme Lohéac , Emmanuel Trélat , Enrique Zuazua
{"title":"Nonnegative control of finite-dimensional linear systems","authors":"Jérôme Lohéac ,&nbsp;Emmanuel Trélat ,&nbsp;Enrique Zuazua","doi":"10.1016/j.anihpc.2020.07.004","DOIUrl":"10.1016/j.anihpc.2020.07.004","url":null,"abstract":"<div><p>We consider the controllability problem for finite-dimensional linear autonomous control systems with nonnegative controls. Despite the Kalman condition, the unilateral nonnegativity<span><span><span> control constraint may cause a positive minimal controllability time. When this happens, we prove that, if the matrix of the system has a real eigenvalue, then there is a minimal time control in the space of </span>Radon measures, which consists of a finite sum of Dirac impulses. When all eigenvalues are real, this control is unique and the number of impulses is less than half the dimension of the space. We also focus on the control system corresponding to a finite-difference </span>spatial discretization of the one-dimensional heat equation with Dirichlet boundary controls, and we provide numerical simulations.</span></p></div>","PeriodicalId":55514,"journal":{"name":"Annales De L Institut Henri Poincare-Analyse Non Lineaire","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2021-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.anihpc.2020.07.004","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82338356","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: 6
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