发布求助
文献互助 智能选刊 最新文献

Annals of Pde最新文献

筛选
英文 中文
Lipschitz Regularity of Fractional p-Laplacian 分数阶p-拉普拉斯算子的Lipschitz正则性
IF 2.6 1区 数学
Annals of Pde Pub Date : 2025-09-26 DOI: 10.1007/s40818-025-00220-4
Anup Biswas, Erwin Topp
{"title":"Lipschitz Regularity of Fractional p-Laplacian","authors":"Anup Biswas,&nbsp;Erwin Topp","doi":"10.1007/s40818-025-00220-4","DOIUrl":"10.1007/s40818-025-00220-4","url":null,"abstract":"<div><p>In this article, we investigate the Hölder regularity of the fractional <span>(p)</span>-Laplace equation of the form <span>((-Delta_p)^s u=f)</span> where <span>(p &gt; 1, sin (0, 1))</span> and <span>(fin L^infty_{rm loc}(Omega))</span>. Specifically, we prove that <span>(uin C^{0, gamma_circ}_{rm loc}(Omega))</span> for <span>(gamma_circ=min{1, frac{sp}{p-1}})</span>, provided that <span>(frac{sp}{p-1}neq 1)</span>. In particular, it shows that <span>(u)</span> is locally Lipschitz for <span>(frac{sp}{p-1} &gt; 1)</span>. Moreover, we show that for <span>(frac{sp}{p-1}=1)</span>, the solution is locally Lipschitz, provided that <span>(f)</span> is locally Hölder continuous. Additionally, we discuss further regularity results for the fractional double-phase problems.</p></div>","PeriodicalId":36382,"journal":{"name":"Annals of Pde","volume":"11 2","pages":""},"PeriodicalIF":2.6,"publicationDate":"2025-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145170322","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
Linear Landau Damping for the Vlasov-Maxwell System in (mathbb{R}^3) Vlasov-Maxwell系统的线性朗道阻尼 (mathbb{R}^3)
IF 2.6 1区 数学
Annals of Pde Pub Date : 2025-09-24 DOI: 10.1007/s40818-025-00217-z
Daniel Han-Kwan, Toan T. Nguyen, Frédéric Rousset
{"title":"Linear Landau Damping for the Vlasov-Maxwell System in (mathbb{R}^3)","authors":"Daniel Han-Kwan,&nbsp;Toan T. Nguyen,&nbsp;Frédéric Rousset","doi":"10.1007/s40818-025-00217-z","DOIUrl":"10.1007/s40818-025-00217-z","url":null,"abstract":"<div>\u0000 \u0000 <p>In this work, we consider the relativistic Vlasov-Maxwell system, linearized around a spatially homogeneous equilibrium, set in the whole space <span>(mathbb{R}^3 times mathbb{R}^3)</span>. The equilibrium is assumed to belong to a class of radial, smooth, rapidly decaying functions. Under appropriate conditions on the initial data, we prove algebraic decay (of dispersive nature) for the electromagnetic field. For the electric scalar potential, the leading behavior is driven by a dispersive wave packet with non-degenerate phase and compactly supported amplitude, while for the magnetic vector potential, it is driven by a wave packet whose phase behaves globally like the one of Klein-Gordon and the amplitude has unbounded support.</p>\u0000 </div>","PeriodicalId":36382,"journal":{"name":"Annals of Pde","volume":"11 2","pages":""},"PeriodicalIF":2.6,"publicationDate":"2025-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s40818-025-00217-z.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145169533","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
Nontrivial Global Solutions to Some Quasilinear Wave Equations in Three Space Dimensions 三维拟线性波动方程的非平凡整体解
IF 2.6 1区 数学
Annals of Pde Pub Date : 2025-08-25 DOI: 10.1007/s40818-025-00205-3
Dongxiao Yu
{"title":"Nontrivial Global Solutions to Some Quasilinear Wave Equations in Three Space Dimensions","authors":"Dongxiao Yu","doi":"10.1007/s40818-025-00205-3","DOIUrl":"10.1007/s40818-025-00205-3","url":null,"abstract":"<div><p>In this paper, we seek to construct nontrivial global solutions to some quasilinear wave equations in three space dimensions. We first present a conditional result on the construction of nontrivial global solutions to a general system of quasilinear wave equations. Assuming that a global solution to the geometric reduced system exists and satisfies several well-chosen pointwise estimates, we find a matching exact global solution to the original wave equations. Such a conditional result is then applied to two types of equations which are of great interest. One is John’s counterexamples <span>(Box u=u_t^2)</span> or <span>(Box u=u_t u_{tt})</span>, and the other is the 3D compressible Euler equations with no vorticity. We explicitly construct global solutions to the corresponding geometric reduced systems and show that these global solutions satisfy the required pointwise bounds. As a result, there exists a large family of nontrivial global solutions to these two types of equations.</p></div>","PeriodicalId":36382,"journal":{"name":"Annals of Pde","volume":"11 2","pages":""},"PeriodicalIF":2.6,"publicationDate":"2025-08-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s40818-025-00205-3.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144897030","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
Dissipative Euler Flows Originating from Circular Vortex Filaments 耗散欧拉流起源于圆涡细丝
IF 2.6 1区 数学
Annals of Pde Pub Date : 2025-07-30 DOI: 10.1007/s40818-025-00211-5
Francisco Gancedo, Antonio Hidalgo-Torné, Francisco Mengual
{"title":"Dissipative Euler Flows Originating from Circular Vortex Filaments","authors":"Francisco Gancedo,&nbsp;Antonio Hidalgo-Torné,&nbsp;Francisco Mengual","doi":"10.1007/s40818-025-00211-5","DOIUrl":"10.1007/s40818-025-00211-5","url":null,"abstract":"<div><p>In this paper, we prove the first existence result of weak solutions to the 3D Euler equation with initial vorticity concentrated in a circle and velocity field in <span>(C([0,T],L^{2^-}))</span>. The energy becomes finite and decreasing for positive times, with vorticity concentrated in a ring that thickens and moves in the direction of the symmetry axis. With our approach, there is no need to mollify the initial data or to rescale the time variable. We overcome the singularity of the initial data by applying convex integration within the appropriate time-weighted space.</p></div>","PeriodicalId":36382,"journal":{"name":"Annals of Pde","volume":"11 2","pages":""},"PeriodicalIF":2.6,"publicationDate":"2025-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s40818-025-00211-5.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145171748","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
Long Time Regularity for 3D Gravity Waves with Vorticity 具有涡度的三维重力波的长时间规律性
IF 2.6 1区 数学
Annals of Pde Pub Date : 2025-07-21 DOI: 10.1007/s40818-025-00206-2
Daniel Ginsberg, Fabio Pusateri
{"title":"Long Time Regularity for 3D Gravity Waves with Vorticity","authors":"Daniel Ginsberg,&nbsp;Fabio Pusateri","doi":"10.1007/s40818-025-00206-2","DOIUrl":"10.1007/s40818-025-00206-2","url":null,"abstract":"<div><p>We consider the Cauchy problem for the full free boundary Euler equations in 3d with an initial small velocity of size <span>(O(varepsilon_0))</span>, in a moving domain which is initially an <span>(O(varepsilon_0))</span> perturbation of a flat interface. We assume that the initial vorticity is of size <span>(O(varepsilon_1))</span> and prove a regularity result up to times of the order <span>(varepsilon_1^{-1+})</span>, independent of <span>({varepsilon _0})</span>. A key part of our proof is a normal form type argument for the vorticity equation; this needs to be performed in the full three dimensional domain and is necessary to effectively remove the irrotational components from the quadratic stretching terms and uniformly control the vorticity. Another difficulty is to obtain sharp decay for the irrotational component of the velocity and the interface; to do this we perform a dispersive analysis on the boundary equations, which are forced by a singular contribution from the rotational component of the velocity. As a corollary of our result, when <span>({varepsilon _1})</span> goes to zero we recover the celebrated global regularity results of Wu (Invent. Math. 2012) and Germain, Masmoudi and Shatah (Ann. of Math. 2013) in the irrotational case.</p></div>","PeriodicalId":36382,"journal":{"name":"Annals of Pde","volume":"11 2","pages":""},"PeriodicalIF":2.6,"publicationDate":"2025-07-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145168277","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
The Reverse Burnett Conjecture for Null Dusts 零尘的逆伯内特猜想
IF 2.6 1区 数学
Annals of Pde Pub Date : 2025-07-11 DOI: 10.1007/s40818-025-00213-3
Arthur Touati
{"title":"The Reverse Burnett Conjecture for Null Dusts","authors":"Arthur Touati","doi":"10.1007/s40818-025-00213-3","DOIUrl":"10.1007/s40818-025-00213-3","url":null,"abstract":"<div><p>Given a regular solution <span>(mathbf{g}_0)</span> of the Einstein-null dusts system without restriction on the number of dusts, we construct families of solutions <span>((mathbf{g}_lambda)_{lambdain(0,1]})</span> of the Einstein vacuum equations such that <span>(mathbf{g}_lambda-mathbf{g}_0)</span> and <span>(partial(mathbf{g}_lambda-mathbf{g}_0))</span> converges respectively strongly and weakly to 0 when <span>(lambdato0)</span>. Our construction, based on a multiphase geometric optics ansatz, thus extends the validity of the reverse Burnett conjecture without symmetry to a large class of massless kinetic spacetimes. In order to deal with the finite but arbitrary number of direction of oscillations we work in a generalised wave gauge and control precisely the self-interaction of each wave but also the interaction of waves propagating in different null directions, relying crucially on the non-linear structure of the Einstein vacuum equations. We also provide the construction of oscillating initial data solving the vacuum constraint equations and which are consistent with the spacetime ansatz.</p></div>","PeriodicalId":36382,"journal":{"name":"Annals of Pde","volume":"11 2","pages":""},"PeriodicalIF":2.6,"publicationDate":"2025-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145165129","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
Pseudolocality and Uniqueness of Ricci Flow on Almost Euclidean Noncompact Manifolds 几乎欧几里德非紧流形上Ricci流的伪局域性和唯一性
IF 2.6 1区 数学
Annals of Pde Pub Date : 2025-07-08 DOI: 10.1007/s40818-025-00216-0
Liang Cheng, Yongjia Zhang
{"title":"Pseudolocality and Uniqueness of Ricci Flow on Almost Euclidean Noncompact Manifolds","authors":"Liang Cheng,&nbsp;Yongjia Zhang","doi":"10.1007/s40818-025-00216-0","DOIUrl":"10.1007/s40818-025-00216-0","url":null,"abstract":"<div><p>In this paper, we prove a pseudolocality-type theorem for <span>(mathcal L)</span>-complete noncompact Ricci flow which may not have bounded sectional curvature; with the help of it we study the uniqueness of the Ricci flow on noncompact manifolds. In particular, we prove the strong uniqueness theorem for the <span>(mathcal L)</span>-complete Ricci flow on the Euclidean space. This partially answers a question proposed by B-L. Chen (J Differ Geom 82(2):363–382, 2009).</p></div>","PeriodicalId":36382,"journal":{"name":"Annals of Pde","volume":"11 2","pages":""},"PeriodicalIF":2.6,"publicationDate":"2025-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145162981","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
Vorticity Blowup in Compressible Euler Equations in (mathbb{R}^d, d geq 3) 可压缩欧拉方程中的涡量爆破 (mathbb{R}^d, d geq 3)
IF 2.6 1区 数学
Annals of Pde Pub Date : 2025-07-08 DOI: 10.1007/s40818-025-00210-6
Jiajie Chen
{"title":"Vorticity Blowup in Compressible Euler Equations in (mathbb{R}^d, d geq 3)","authors":"Jiajie Chen","doi":"10.1007/s40818-025-00210-6","DOIUrl":"10.1007/s40818-025-00210-6","url":null,"abstract":"<div><p>We prove finite-time vorticity blowup in the compressible Euler equations in <span>(mathbb{R}^d)</span> for any <span>(d geq 3)</span>, starting from smooth, localized, and non-vacuous initial data. This is achieved by lifting the vorticity blowup result from (Chen arXiv preprint arXiv: 2407.06455, 2024) in <span>(mathbb{R}^2)</span> to <span>(mathbb{R}^d)</span> and utilizing the axisymmetry in <span>(mathbb{R}^d)</span>. At the time of the first singularity, both vorticity blowup and implosion occur on a sphere <span>(S^{d-2})</span>. Additionally, the solution exhibits a non-radial implosion, accompanied by a stable swirl velocity that is sufficiently strong to initially dominate the non-radial components and to generate the vorticity blowup.</p></div>","PeriodicalId":36382,"journal":{"name":"Annals of Pde","volume":"11 2","pages":""},"PeriodicalIF":2.6,"publicationDate":"2025-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145162982","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
Finite Time Singularities to the 3D Incompressible Euler Equations for Solutions in(:C^{infty}(mathbb{R}^3 setminus {0})cap C^{1,alpha}cap L^2) 中的三维不可压缩欧拉方程解的有限时间奇异性(:C^{infty}(mathbb{R}^3 setminus {0})cap C^{1,alpha}cap L^2)
IF 2.6 1区 数学
Annals of Pde Pub Date : 2025-07-07 DOI: 10.1007/s40818-025-00214-2
Diego Córdoba, Luis Martinez-Zoroa, Fan Zheng
{"title":"Finite Time Singularities to the 3D Incompressible Euler Equations for Solutions in(:C^{infty}(mathbb{R}^3 setminus {0})cap C^{1,alpha}cap L^2)","authors":"Diego Córdoba,&nbsp;Luis Martinez-Zoroa,&nbsp;Fan Zheng","doi":"10.1007/s40818-025-00214-2","DOIUrl":"10.1007/s40818-025-00214-2","url":null,"abstract":"<div><p>We introduce a novel mechanism that reveals finite time singularities within the 1D De Gregorio model and the 3D incompressible Euler equations. Remarkably, we do not construct our blow up using self-similar coordinates, but build it from infinitely many regions with vorticity, separated by vortex-free regions in between. It yields solutions of the 3D incompressible Euler equations in <span>(mathbb{R}^3times [-T,0])</span> such that the velocity is in the space <span>(C^{infty}(mathbb{R}^3 setminus {0})cap C^{1,alpha}cap L^2)</span> where <span>(0 &lt; alpha ll 1)</span> for times <span>(tin (-T,0))</span> and is not <span>(C^1)</span> at time 0.</p></div>","PeriodicalId":36382,"journal":{"name":"Annals of Pde","volume":"11 2","pages":""},"PeriodicalIF":2.6,"publicationDate":"2025-07-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s40818-025-00214-2.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145163230","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
On Existence of Sadovskii Vortex Patch: A Touching Pair of Symmetric Counter-Rotating Uniform Vortices 关于Sadovskii涡片的存在性：对称反旋转均匀涡的接触对
IF 2.6 1区 数学
Annals of Pde Pub Date : 2025-07-01 DOI: 10.1007/s40818-025-00212-4
Kyudong Choi, In-Jee Jeong, Young-Jin Sim
{"title":"On Existence of Sadovskii Vortex Patch: A Touching Pair of Symmetric Counter-Rotating Uniform Vortices","authors":"Kyudong Choi,&nbsp;In-Jee Jeong,&nbsp;Young-Jin Sim","doi":"10.1007/s40818-025-00212-4","DOIUrl":"10.1007/s40818-025-00212-4","url":null,"abstract":"<div><p>The Sadovskii vortex patch is a traveling wave for the two-dimensional incompressible Euler equations consisting of an odd symmetric pair of vortex patches touching the symmetry axis. Its existence was first suggested by numerical computations of Sadovskii in [J. Appl. Math. Mech., 1971], and has gained significant interest due to its relevance in inviscid limit of planar flows via Prandtl–Batchelor theory and as the asymptotic state for vortex ring dynamics. In this work, we prove the existence of a Sadovskii vortex patch, by solving the energy maximization problem under the exact impulse condition and an upper bound on the circulation.</p></div>","PeriodicalId":36382,"journal":{"name":"Annals of Pde","volume":"11 2","pages":""},"PeriodicalIF":2.6,"publicationDate":"2025-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s40818-025-00212-4.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145160540","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
下一页 尾页
0
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整，为了账户安全，请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
请完成安全验证×
相关产品
×
本文献相关产品
联系我们：info@booksci.cn Book学术提供免费学术资源搜索服务，方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号：604180095
Book学术官方微信