Annals of Pde最新文献

Global-in-Time Weak Solutions for an Inviscid Free Surface Fluid-Structure Problem Without Damping

IF 2.4 1区数学

Annals of Pde Pub Date : 2025-05-13 DOI: 10.1007/s40818-025-00207-1

Thomas Alazard, Igor Kukavica, Amjad Tuffaha

引用次数: 0

Wellposedness of the Electron MHD Without Resistivity for Large Perturbations of the Uniform Magnetic Field 均匀磁场大扰动下无电阻电子MHD的适位性

IF 2.4 1区数学

Annals of Pde Pub Date : 2025-05-06 DOI: 10.1007/s40818-025-00198-z

In-Jee Jeong, Sung-Jin Oh

{"title":"Wellposedness of the Electron MHD Without Resistivity for Large Perturbations of the Uniform Magnetic Field","authors":"In-Jee Jeong, Sung-Jin Oh","doi":"10.1007/s40818-025-00198-z","DOIUrl":"10.1007/s40818-025-00198-z","url":null,"abstract":"<div>We prove the local wellposedness of the Cauchy problems for the electron magnetohydrodynamics equations (E-MHD) without resistivity for possibly large perturbations of nonzero uniform magnetic fields. While the local wellposedness problem for (E-MHD) has been extensively studied in the presence of resistivity (which provides dissipative effects), this seems to be the first such result without resistivity. (E-MHD) is a fluid description of plasma in small scales where the motion of electrons relative to ions is significant. Mathematically, it is a quasilinear dispersive equation with nondegenerate but nonelliptic second-order principal term. Our result significantly improves upon the straightforward adaptation of the classical work of Kenig–Ponce–Rolvung–Vega on the quasilinear ultrahyperbolic Schrödinger equations, as the regularity and decay assumptions on the initial data are greatly weakened to the level analogous to the recent work of Marzuola–Metcalfe–Tataru in the case of elliptic principal term.A key ingredient of our proof is a simple observation about the relationship between the size of a symbol and the operator norm of its quantization as a pseudodifferential operator when restricted to high frequencies. This allows us to localize the (non-classical) pseudodifferential renormalization operator considered by Kenig–Ponce–Rolvung–Vega, and produce instead a classical pseudodifferential renormalization operator. We furthermore incorporate the function space framework of Marzuola–Metcalfe–Tataru to the present case of nonelliptic principal term.</div>","PeriodicalId":36382,"journal":{"name":"Annals of Pde","volume":"11 1","pages":""},"PeriodicalIF":2.4,"publicationDate":"2025-05-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s40818-025-00198-z.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143913857","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

IF 2.4 1区数学

Annals of Pde Pub Date : 2025-05-06 DOI: 10.1007/s40818-025-00203-5

Feng Shao, Dongyi Wei, Zhifei Zhang

引用次数: 0

Construction of Type I-Log Blowup for the Keller-Segel System in Dimensions 3 and 4 3维和4维Keller-Segel系统的I-Log型爆破构造

IF 2.4 1区数学

Annals of Pde Pub Date : 2025-04-18 DOI: 10.1007/s40818-025-00202-6

Van Tien Nguyen, Nejla Nouaili, Hatem Zaag

引用次数: 0

Stability for Linearized Gravity on the Kerr Spacetime 克尔时空上线性化重力的稳定性

IF 2.4 1区数学

Annals of Pde Pub Date : 2025-04-15 DOI: 10.1007/s40818-024-00193-w

Lars Andersson, Thomas Bäckdahl, Pieter Blue, Siyuan Ma

引用次数: 0

Stable Space-Like Singularity Formation for Axi-symmetric and Polarized Near-Schwarzschild Black Hole Interiors 阿西对称和极化近施瓦兹柴尔德黑洞内部的稳定类空奇点形成

IF 2.4 1区数学

Annals of Pde Pub Date : 2025-04-02 DOI: 10.1007/s40818-025-00200-8

Spyros Alexakis, Grigorios Fournodavlos

{"title":"Stable Space-Like Singularity Formation for Axi-symmetric and Polarized Near-Schwarzschild Black Hole Interiors","authors":"Spyros Alexakis, Grigorios Fournodavlos","doi":"10.1007/s40818-025-00200-8","DOIUrl":"10.1007/s40818-025-00200-8","url":null,"abstract":"<div>We show a stability result for the Schwarzschild singularity (inside the black hole region) for the Einstein vacuum equations (EVE). The result is proven in the class of polarized axial symmetry, under perturbations of the Schwarzschild data induced on a hypersurface ({r=epsilon }), (epsilon<<2M). Our result is only partly a stability result, in that we show that while a (space-like) singularity persists under perturbations as above, the behavior of the metric approaching the singularity is much more involved than for the Schwarzschild solution. Indeed, we find that the solution displays asymptocially-velocity-term-dominated dynamics and approaches a different Kasner solution at each point of the singularity. These Kasner-type asymptotics are very far from isotropic, since (as in Schwarzschild) there are two contracting directions and one expanding one. Our proof relies on energy methods and on a new approach to the EVE in axial symmetry, which we believe has wider applicability: In this symmetry class and under a suitable geodesic gauge, the EVE can be studied as a free wave coupled to (nonlinear) ODEs, which couple the geometry of the projected, 2+1 space-time to the free wave. The fact that the nonlinear part of the Einstein equations is described by ODEs lies at the heart of how one can overcome a certain linear instability exhibited by the singularity.</div>","PeriodicalId":36382,"journal":{"name":"Annals of Pde","volume":"11 1","pages":""},"PeriodicalIF":2.4,"publicationDate":"2025-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143761735","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

Time-Global Regularity of the Navier–Stokes System with Hyper-Dissipation: Turbulent Scenario 具有超耗散的Navier-Stokes系统的时-全局正则性：湍流情景

IF 2.4 1区数学

Annals of Pde Pub Date : 2025-03-06 DOI: 10.1007/s40818-025-00199-y

Zoran Grujić, Liaosha Xu

{"title":"Time-Global Regularity of the Navier–Stokes System with Hyper-Dissipation: Turbulent Scenario","authors":"Zoran Grujić, Liaosha Xu","doi":"10.1007/s40818-025-00199-y","DOIUrl":"10.1007/s40818-025-00199-y","url":null,"abstract":"<div>The question of whether the hyper-dissipative (HD) Navier-Stokes (NS) system can exhibit spontaneous formation of singularities in the super-critical regime–the hyperviscous effects being represented by a fractional power of the Laplacian, say (beta ), confined to interval (bigl (1, frac{5}{4}bigr ))–has been a major open problem in the mathematical fluid dynamics since the foundational work of J.L. Lions in 1960s. In this work, an evidence of criticality of the Laplacian is presented, more precisely, a class of plausible blow-up scenarios is ruled out as soon as (beta ) is greater than one. While the framework is based on the ‘scale of sparseness’ of the super-level sets of the positive and negative parts of the components of the higher-order derivatives of the velocity previously introduced by the authors, a major novelty in the current work is classification of the HD flows near a potential spatiotemporal singularity in two main categories, ‘homogeneous’ (the case consistent with a near-steady behavior) and ‘non-homogenous’ (the case consistent with the formation and decay of turbulence). The main theorem states that in the non-homogeneous case any (beta ) greater than one prevents a singularity. In order to illustrate the impact of this result in a methodology-free setting, a two-parameter family of dynamically rescaled blow-up profiles is considered, and it is shown that as soon as (beta ) is greater than one, a new region in the parameter space is ruled out. More importantly, the region is a neighborhood (in the parameter space) of the self-similar profile, i.e., the approximately self-similar blow-up, a prime suspect in possible singularity formation, is ruled out for all HD NS models.</div>","PeriodicalId":36382,"journal":{"name":"Annals of Pde","volume":"11 1","pages":""},"PeriodicalIF":2.4,"publicationDate":"2025-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s40818-025-00199-y.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143553784","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

Inviscid Damping of Monotone Shear Flows for 2D Inhomogeneous Euler Equation with Non-Constant Density in a Finite Channel 有限通道中非常密度二维非齐次欧拉方程单调剪切流的无粘阻尼

IF 2.4 1区数学

Annals of Pde Pub Date : 2025-01-31 DOI: 10.1007/s40818-025-00197-0

Weiren Zhao

引用次数: 0

Transport of Nonlinear Oscillations Along Rays that Graze a Convex Obstacle to any Order 非线性振荡沿任意阶掠过凸障碍物的射线的输运

IF 2.4 1区数学

Annals of Pde Pub Date : 2025-01-27 DOI: 10.1007/s40818-025-00195-2

Jian Wang, Mark Williams

{"title":"Transport of Nonlinear Oscillations Along Rays that Graze a Convex Obstacle to any Order","authors":"Jian Wang, Mark Williams","doi":"10.1007/s40818-025-00195-2","DOIUrl":"10.1007/s40818-025-00195-2","url":null,"abstract":"<div>We provide a geometric optics description in spaces of low regularity, (L^2) and (H^1), of the transport of oscillations in solutions to linear and some semilinear second-order hyperbolic boundary problems along rays that graze the boundary of a convex obstacle to arbitrarily high finite or infinite order. The fundamental motivating example is the case where the spacetime manifold is (M=(mathbb {R}^nsetminus mathcal {O})times mathbb {R}_t), where (mathcal {O}subset mathbb {R}^n) is an open convex obstacle with (C^infty ) boundary, and the governing hyperbolic operator is the wave operator (Box :=Delta -partial _t^2). The main theorem says that high frequency exact solutions are well approximated in spaces of low regularity by approximate solutions constructed from fairly explicit solutions to relatively simple profile equations. The theorem has two main assumptions. The first is that the grazing set, that is, the set of points on the spacetime boundary at which incoming characteristics meet the boundary tangentially, is a codimension two, (C^1) submanifold of spacetime. The second is that the reflected flow map, which sends points on the spacetime boundary forward in time to points on reflected and grazing rays, is injective and has appropriate regularity properties near the grazing set. Both assumptions are in general hard to verify, but we show that they are satisfied for the diffraction of incoming plane waves by a large class of strictly convex obstacles in all dimensions, involving grazing points of arbitrarily high finite or infinite order.</div>","PeriodicalId":36382,"journal":{"name":"Annals of Pde","volume":"11 1","pages":""},"PeriodicalIF":2.4,"publicationDate":"2025-01-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143109681","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

Calderón–Zygmund Estimates for the Fractional p-Laplacian Calderón-Zygmund分数阶p-拉普拉斯算子的估计

IF 2.4 1区数学

Annals of Pde Pub Date : 2025-01-25 DOI: 10.1007/s40818-025-00196-1

Lars Diening, Simon Nowak

引用次数: 0