Annals of Pde最新文献

Stability of the Catenoid for the Hyperbolic Vanishing Mean Curvature Equation in 4 Spatial Dimensions 双曲型平均曲率消失方程链面在4维空间中的稳定性

IF 3 1区数学

Annals of Pde Pub Date : 2026-10-13 DOI: 10.1007/s40818-026-00256-0

Ning Tang

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引用次数: 0

Spectral Instability in the Smooth Ponomarenko Dynamo 光滑波诺马连科发电机的谱不稳定性

IF 3 1区数学

Annals of Pde Pub Date : 2026-10-09 DOI: 10.1007/s40818-026-00255-1

Víctor Navarro-Fernández, David Villringer

{"title":"Spectral Instability in the Smooth Ponomarenko Dynamo","authors":"Víctor Navarro-Fernández, David Villringer","doi":"10.1007/s40818-026-00255-1","DOIUrl":"10.1007/s40818-026-00255-1","url":null,"abstract":"<div>We consider the kinematic dynamo equations for a passive vector in (mathcal {M} times mathbb {T} subseteq mathbb {R}^2 times mathbb {T}) describing the evolution of a magnetic field with resistivity (varepsilon > 0), that is transported by a given velocity field. For a broad class of (C^3) velocity fields with helical geometry, we establish the existence of solutions that exhibit exponential growth over time. We construct an unstable eigenmode via detailed resolvent estimates of the corresponding linear operator, which we carry out by introducing suitable Green’s functions that accurately approximate the local behaviour of the true system. This approach yields an explicit asymptotic expression for the growing mode, providing a sharp description of the instability mechanism. We first derive the results with (mathcal {M}=mathbb {R}^2) for a large class of velocity fields that includes finite energy examples. We then consider the case of domains with boundary, where (mathcal {M}times mathbb {T}) denotes a periodic cylinder, annular cylinder, or the exterior of a cylinder, with the boundary conditions of perfectly conducting walls. Our results offer a rigorous and sharp mathematical justification for the physically conjectured process by which helical flows can sustain magnetic field generation in the Ponomarenko dynamo, with growth rate of order (varepsilon ^{1/3}).</div>","PeriodicalId":36382,"journal":{"name":"Annals of Pde","volume":"12 2","pages":""},"PeriodicalIF":3.0,"publicationDate":"2026-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s40818-026-00255-1.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149132770","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Enhanced Lifespan Bounds for 1D Quasilinear Klein–Gordon Flows 一维拟线性Klein-Gordon流的改进寿命界

IF 3 1区数学

Annals of Pde Pub Date : 2026-10-09 DOI: 10.1007/s40818-026-00250-6

Hongjing Huang, Mihaela Ifrim, Daniel Tataru

引用次数: 0

Decay Estimates of Wave Equations in Un-isotropic Media 非各向同性介质中波动方程的衰减估计

IF 3 1区数学

Annals of Pde Pub Date : 2026-10-07 DOI: 10.1007/s40818-026-00259-x

Sergiu Klainerman, Xuecheng Wang

引用次数: 0

Fully Non-linear Elliptic Equations on Complex Manifolds 复流形上的完全非线性椭圆方程

IF 3 1区数学

Annals of Pde Pub Date : 2026-10-05 DOI: 10.1007/s40818-026-00249-z

Rirong Yuan

引用次数: 0

Nonradial Stability of Self-Similar Blowup to the Keller–Segel Equation in Three Dimensions 三维Keller-Segel方程自相似爆破的非径向稳定性

IF 3 1区数学

Annals of Pde Pub Date : 2026-10-01 DOI: 10.1007/s40818-026-00257-z

Zexing Li, Tao Zhou

引用次数: 0

Asymmetric Self-Similar Spiral Solutions of 2-D Incompressible Euler Equations 二维不可压缩欧拉方程的非对称自相似螺旋解

IF 3 1区数学

Annals of Pde Pub Date : 2026-09-26 DOI: 10.1007/s40818-026-00254-2

Hyungjun Choi

引用次数: 0

Improved Moduli of Continuity for Degenerate Phase Transitions 退化相变的改进连续模。

IF 3 1区数学

Annals of Pde Pub Date : 2026-09-05 DOI: 10.1007/s40818-026-00253-3

Ugo Gianazza, Naian Liao, José Miguel Urbano

引用次数: 0

Asymptotic Analysis of Small Energy Breathers for the Nonlinear Klein–Gordon Equation 非线性Klein-Gordon方程小能量呼吸子的渐近分析

IF 3 1区数学

Annals of Pde Pub Date : 2026-08-21 DOI: 10.1007/s40818-026-00251-5

Michał Kowalczyk, Yvan Martel

引用次数: 0

Exact Boundary Controllability of the 3D and 2D Incompressible Ideal MHD System 三维和二维不可压缩理想MHD系统的精确边界可控性

IF 3 1区数学

Annals of Pde Pub Date : 2026-08-05 DOI: 10.1007/s40818-026-00238-2

Igor Kukavica, Wojciech Ożański

{"title":"Exact Boundary Controllability of the 3D and 2D Incompressible Ideal MHD System","authors":"Igor Kukavica, Wojciech Ożański","doi":"10.1007/s40818-026-00238-2","DOIUrl":"10.1007/s40818-026-00238-2","url":null,"abstract":"<div>We consider the three-dimensional ideal MHD system on a domain (Omega ' subset mathbb {R}^3) with an open subset (Gamma ) of the boundary (partial Omega ') where we prescribe both (ucdot textsf{n}) and (bcdot textsf{n}), while (ucdot textsf{n}= bcdot textsf{n}=0) on (partial Omega ' setminus Gamma ). We prove boundary controllability of the system, namely that we can prescribe the boundary data such that the unique solution of the system with an initial state ((u_0,b_0)) achieves another state ((u_1,b_1)) in a finite time, where (u_0,b_0,u_1,b_1) are arbitrary divergence-free vector fields satisfying impermeability boundary condition and which are extendible to vector fields with the same properties on any bounded domain obtained by extension of (Omega ') via (Gamma ). As a byproduct, we give the first local well-posedness proof for the incompressible ideal MHD system which does not use Elsasser variables and is thus applicable to any bounded domain with sufficient Sobolev regularity. We also provide a new, simpler control for the two-dimensional ideal MHD system.</div>","PeriodicalId":36382,"journal":{"name":"Annals of Pde","volume":"12 2","pages":""},"PeriodicalIF":3.0,"publicationDate":"2026-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148750919","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