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

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Normalized solutions of $L^2$-supercritical NLS equations on compact metric graphs 紧度量图上的L^2 -超临界NLS方程的归一化解
IF 1.9 1区 数学
Annales De L Institut Henri Poincare-Analyse Non Lineaire Pub Date : 2022-04-03 DOI: 10.4171/aihpc/88
Xiaojun Chang, L. Jeanjean, N. Soave
{"title":"Normalized solutions of $L^2$-supercritical NLS equations on compact metric graphs","authors":"Xiaojun Chang, L. Jeanjean, N. Soave","doi":"10.4171/aihpc/88","DOIUrl":"https://doi.org/10.4171/aihpc/88","url":null,"abstract":"This paper is devoted to the existence of non-trivial bound states of prescribed mass for the mass-supercritical nonlinear Schr\"odinger equation on compact metric graphs. The investigation is based upon a general variational principle which combines the monotonicity trick and a min-max theorem with second order information, and upon the blow-up analysis of bound states with prescribed mass and bounded Morse index.","PeriodicalId":55514,"journal":{"name":"Annales De L Institut Henri Poincare-Analyse Non Lineaire","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2022-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85902482","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
Dynamics of mean-field bosons at positive temperature 正温度下平均场玻色子动力学
IF 1.9 1区 数学
Annales De L Institut Henri Poincare-Analyse Non Lineaire Pub Date : 2022-03-31 DOI: 10.4171/aihpc/93
Marco Caporaletti, A. Deuchert, B. Schlein
{"title":"Dynamics of mean-field bosons at positive temperature","authors":"Marco Caporaletti, A. Deuchert, B. Schlein","doi":"10.4171/aihpc/93","DOIUrl":"https://doi.org/10.4171/aihpc/93","url":null,"abstract":"We study the time evolution of an initially trapped weakly interacting Bose gas at positive temperature, after the trapping potential has been switched off. It has been recently shown in arXiv:2009.00992 that the one-particle density matrix of Gibbs states of the interacting trapped gas is given, to leading order in $N$, as $N to infty$, by the one of the ideal gas, with the condensate wave function replaced by the minimizer of the Hartree energy functional. We show that this structure is stable with respect to the many-body evolution in the following sense: the dynamics can be approximated in terms of the time-dependent Hartree equation for the condensate wave function and in terms of the free evolution for the thermally excited particles. The main technical novelty of our work is the use of the Hartree-Fock-Bogoliubov equations to define a fluctuation dynamics.","PeriodicalId":55514,"journal":{"name":"Annales De L Institut Henri Poincare-Analyse Non Lineaire","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2022-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78076260","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
Optimal decay rate for higher-order derivatives of the solution to the Lagrangian-averaged Navier–Stokes-$alpha$ equation in $mathbb{R}^3$ $mathbb{R}^3$中拉格朗日平均Navier-Stokes -$alpha$方程解的高阶导数的最优衰减率
IF 1.9 1区 数学
Annales De L Institut Henri Poincare-Analyse Non Lineaire Pub Date : 2022-03-11 DOI: 10.4171/aihpc/19
Jincheng Gao, Zeyu Lyu, Z. Yao
{"title":"Optimal decay rate for higher-order derivatives of the solution to the Lagrangian-averaged Navier–Stokes-$alpha$ equation in $mathbb{R}^3$","authors":"Jincheng Gao, Zeyu Lyu, Z. Yao","doi":"10.4171/aihpc/19","DOIUrl":"https://doi.org/10.4171/aihpc/19","url":null,"abstract":"","PeriodicalId":55514,"journal":{"name":"Annales De L Institut Henri Poincare-Analyse Non Lineaire","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2022-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88627027","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
Forward-modulated damping estimates and nonlocalized stability of periodic Lugiato–Lefever waves 周期Lugiato-Lefever波的前调阻尼估计和非定域稳定性
IF 1.9 1区 数学
Annales De L Institut Henri Poincare-Analyse Non Lineaire Pub Date : 2022-03-03 DOI: 10.4171/aihpc/76
K. Zumbrun
{"title":"Forward-modulated damping estimates and nonlocalized stability of periodic Lugiato–Lefever waves","authors":"K. Zumbrun","doi":"10.4171/aihpc/76","DOIUrl":"https://doi.org/10.4171/aihpc/76","url":null,"abstract":"In an interesting recent analysis, Haragus-Johnson-Perkins-de Rijk have shown modulational stability under localized perturbations of steady periodic solutions of the Lugiato-Lefever equation (LLE), in the process pointing out a difficulty in obtaining standard\"nonlinear damping estimates\"on modulated perturbation variables to control regularity of solutions. Here, we point out that in place of standard\"inverse-modulated\"damping estimates, one can alternatively carry out a damping estimate on the\"forward-modulated\"perturbation, noting that norms of forward- and inverse-modulated variables are equivalent modulo absorbable errors, thus recovering the classical argument structure of Johnson-Noble-Rodrigues-Zumbrun for parabolic systems. This observation seems of general use in situations of delicate regularity. Applied in the context of (LLE) it gives the stronger result of stability and asymptotic behavior with respect to nonlocalized perturbations.","PeriodicalId":55514,"journal":{"name":"Annales De L Institut Henri Poincare-Analyse Non Lineaire","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2022-03-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88303458","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
Control of the Schrödinger equation by slow deformations of the domain 控制Schrödinger方程的缓慢变形的领域
IF 1.9 1区 数学
Annales De L Institut Henri Poincare-Analyse Non Lineaire Pub Date : 2022-03-01 DOI: 10.4171/aihpc/86
Alessandro Duca, R. Joly, D. Turaev
{"title":"Control of the Schrödinger equation by slow deformations of the domain","authors":"Alessandro Duca, R. Joly, D. Turaev","doi":"10.4171/aihpc/86","DOIUrl":"https://doi.org/10.4171/aihpc/86","url":null,"abstract":"The aim of this work is to study the controllability of the Schr\"odinger equation begin{equation}label{eq_abstract} ipartial_t u(t)=-Delta u(t)~~~~~text{ on }Omega(t) tag{$ast$} end{equation} with Dirichlet boundary conditions, where $Omega(t)subsetmathbb{R}^N$ is a time-varying domain. We prove the global approximate controllability of eqref{eq_abstract} in $L^2(Omega)$, via an adiabatic deformation $Omega(t)subsetmathbb{R}$ ($tin[0,T]$) such that $Omega(0)=Omega(T)=Omega$. This control is strongly based on the Hamiltonian structure of eqref{eq_abstract} provided by [18], which enables the use of adiabatic motions. We also discuss several explicit interesting controls that we perform in the specific framework of rectangular domains.","PeriodicalId":55514,"journal":{"name":"Annales De L Institut Henri Poincare-Analyse Non Lineaire","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2022-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81656633","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: 4
On threshold solutions of the equivariant Chern–Simons–Schrödinger equation 等变Chern-Simons-Schrödinger方程的阈值解
IF 1.9 1区 数学
Annales De L Institut Henri Poincare-Analyse Non Lineaire Pub Date : 2022-02-25 DOI: 10.4171/aihpc/10
Zexing Li, Bao-ying Liu
{"title":"On threshold solutions of the equivariant Chern–Simons–Schrödinger equation","authors":"Zexing Li, Bao-ying Liu","doi":"10.4171/aihpc/10","DOIUrl":"https://doi.org/10.4171/aihpc/10","url":null,"abstract":"","PeriodicalId":55514,"journal":{"name":"Annales De L Institut Henri Poincare-Analyse Non Lineaire","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2022-02-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74618399","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: 5
Long-time dynamics of a hinged-free plate driven by a nonconservative force 非保守力驱动下无铰板的长时间动力学
IF 1.9 1区 数学
Annales De L Institut Henri Poincare-Analyse Non Lineaire Pub Date : 2022-02-25 DOI: 10.4171/aihpc/13
D. Bonheure, F. Gazzola, I. Lasiecka, J. Webster
{"title":"Long-time dynamics of a hinged-free plate driven by a nonconservative force","authors":"D. Bonheure, F. Gazzola, I. Lasiecka, J. Webster","doi":"10.4171/aihpc/13","DOIUrl":"https://doi.org/10.4171/aihpc/13","url":null,"abstract":"","PeriodicalId":55514,"journal":{"name":"Annales De L Institut Henri Poincare-Analyse Non Lineaire","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2022-02-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85056266","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: 4
Refined asymptotics for the blow-up solution of the complex Ginzburg–Landau equation in the subcritical case 次临界情况下复Ginzburg-Landau方程爆破解的精炼渐近性
IF 1.9 1区 数学
Annales De L Institut Henri Poincare-Analyse Non Lineaire Pub Date : 2022-02-09 DOI: 10.4171/aihpc/2
G. K. Duong, N. Nouaili, H. Zaag
{"title":"Refined asymptotics for the blow-up solution of the complex Ginzburg–Landau equation in the subcritical case","authors":"G. K. Duong, N. Nouaili, H. Zaag","doi":"10.4171/aihpc/2","DOIUrl":"https://doi.org/10.4171/aihpc/2","url":null,"abstract":"","PeriodicalId":55514,"journal":{"name":"Annales De L Institut Henri Poincare-Analyse Non Lineaire","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2022-02-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88946619","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
Uniform asymptotic stability for convection–reaction–diffusion equations in the inviscid limit towards Riemann shocks 黎曼激波下对流-反应-扩散方程无粘极限的一致渐近稳定性
IF 1.9 1区 数学
Annales De L Institut Henri Poincare-Analyse Non Lineaire Pub Date : 2022-01-31 DOI: 10.4171/aihpc/90
Paul Blochas, L. Rodrigues
{"title":"Uniform asymptotic stability for convection–reaction–diffusion equations in the inviscid limit towards Riemann shocks","authors":"Paul Blochas, L. Rodrigues","doi":"10.4171/aihpc/90","DOIUrl":"https://doi.org/10.4171/aihpc/90","url":null,"abstract":"The present contribution proves the asymptotic orbital stability of viscous regularizations of stable Riemann shocks of scalar balance laws, uniformly with respect to the viscosity/diffusion parameter $epsilon$. The uniformity is understood in the sense that all constants involved in the stability statements are uniform and that the corresponding multiscale $epsilon$-dependent topology reduces to the classical $W^{1,infty}$-topology when restricted to functions supported away from the shock location. Main difficulties include that uniformity precludes any use of parabolic regularization to close regularity estimates, that the global-in-time analysis is also spatially multiscale due to the coexistence of nontrivial slow parts with fast shock-layer parts, that the limiting smooth spectral problem (in fast variables) has no spectral gap and that uniformity requires a very precise and unusual design of the phase shift encoding orbital stability. In particular, our analysis builds a phase that somehow interpolates between the hyperbolic shock location prescribed by the Rankine-Hugoniot conditions and the non-uniform shift arising merely from phasing out the non-decaying $0$-mode, as in the classical stability analysis for fronts of reaction-diffusion equations.","PeriodicalId":55514,"journal":{"name":"Annales De L Institut Henri Poincare-Analyse Non Lineaire","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2022-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78829784","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
Homogeneous functions with nowhere-vanishing Hessian determinant 具有不灭黑森行列式的齐次函数
IF 1.9 1区 数学
Annales De L Institut Henri Poincare-Analyse Non Lineaire Pub Date : 2022-01-04 DOI: 10.4171/aihpc/78
Connor Mooney
{"title":"Homogeneous functions with nowhere-vanishing Hessian determinant","authors":"Connor Mooney","doi":"10.4171/aihpc/78","DOIUrl":"https://doi.org/10.4171/aihpc/78","url":null,"abstract":"We prove that functions that are homogeneous of degree $alpha in (0,,1)$ on $mathbb{R}^n$ and have nowhere vanishing Hessian determinant cannot change sign.","PeriodicalId":55514,"journal":{"name":"Annales De L Institut Henri Poincare-Analyse Non Lineaire","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2022-01-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75047050","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
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