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
Dynamics of Apparent Horizon and a Null Comparison Principle 表观地平线动力学和无效比较原则
IF 2.4 1区 数学
Annals of Pde Pub Date : 2024-08-03 DOI: 10.1007/s40818-024-00180-1
Xinliang An, Taoran He
{"title":"Dynamics of Apparent Horizon and a Null Comparison Principle","authors":"Xinliang An,&nbsp;Taoran He","doi":"10.1007/s40818-024-00180-1","DOIUrl":"10.1007/s40818-024-00180-1","url":null,"abstract":"<div><p>This paper investigates the global dynamics of the apparent horizon. We present an approach to establish its existence and its long-term behaviors. Our apparent horizon is constructed by solving the marginally outer trapped surface (MOTS) along each incoming null hypersurface. Based on the nonlinear hyperbolic estimates established in [21] by Klainerman-Szeftel under polarized axial symmetry, we prove that the corresponding apparent horizon is smooth, asymptotically null and converging to the event horizon eventually. To further address the local achronality of the apparent horizon, a new concept, called the <i>null comparison principle</i>, is introduced in this paper. For three typical scenarios of gravitational collapse, our null comparison principle is tested and verified, which guarantees that the apparent horizon must be piecewise spacelike or piecewise null. In addition, we also validate and provide new proofs for several physical laws along the apparent horizon.</p></div>","PeriodicalId":36382,"journal":{"name":"Annals of Pde","volume":"10 2","pages":""},"PeriodicalIF":2.4,"publicationDate":"2024-08-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142409586","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
Well/Ill-Posedness Bifurcation for the Boltzmann Equation with Constant Collision Kernel 具有恒定碰撞内核的玻尔兹曼方程的良好/全拟合分岔
IF 2.4 1区 数学
Annals of Pde Pub Date : 2024-07-24 DOI: 10.1007/s40818-024-00177-w
Xuwen Chen, Justin Holmer
{"title":"Well/Ill-Posedness Bifurcation for the Boltzmann Equation with Constant Collision Kernel","authors":"Xuwen Chen,&nbsp;Justin Holmer","doi":"10.1007/s40818-024-00177-w","DOIUrl":"10.1007/s40818-024-00177-w","url":null,"abstract":"<div><p>We consider the 3D Boltzmann equation with the constant collision kernel. We investigate the well/ill-posedness problem using the methods from nonlinear dispersive PDEs. We construct a family of special solutions, which are neither near equilibrium nor self-similar, to the equation, and prove that the well/ill-posedness threshold in <span>(H^{s})</span> Sobolev space is exactly at regularity <span>(s=1)</span>, despite the fact that the equation is scale invariant at <span>( s=frac{1}{2})</span>.</p></div>","PeriodicalId":36382,"journal":{"name":"Annals of Pde","volume":"10 2","pages":""},"PeriodicalIF":2.4,"publicationDate":"2024-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142413408","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
Small Scale Creation for 2D Free Boundary Euler Equations with Surface Tension 带表面张力的二维自由边界欧拉方程的小尺度创建
IF 2.4 1区 数学
Annals of Pde Pub Date : 2024-07-05 DOI: 10.1007/s40818-024-00179-8
Zhongtian Hu, Chenyun Luo, Yao Yao
{"title":"Small Scale Creation for 2D Free Boundary Euler Equations with Surface Tension","authors":"Zhongtian Hu,&nbsp;Chenyun Luo,&nbsp;Yao Yao","doi":"10.1007/s40818-024-00179-8","DOIUrl":"10.1007/s40818-024-00179-8","url":null,"abstract":"<div><p>In this paper, we study the 2D free boundary incompressible Euler equations with surface tension, where the fluid domain is periodic in <span>(x_1)</span>, and has finite depth. We construct initial data with a flat free boundary and arbitrarily small velocity, such that the gradient of vorticity grows at least double-exponentially for all times during the lifespan of the associated solution. This work generalizes the celebrated result by Kiselev–Šverák [17] to the free boundary setting. The free boundary introduces some major challenges in the proof due to the deformation of the fluid domain and the fact that the velocity field cannot be reconstructed from the vorticity using the Biot-Savart law. We overcome these issues by deriving uniform-in-time control on the free boundary and obtaining pointwise estimates on an approximate Biot-Savart law.</p></div>","PeriodicalId":36382,"journal":{"name":"Annals of Pde","volume":"10 2","pages":""},"PeriodicalIF":2.4,"publicationDate":"2024-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142410053","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
Physical Space Approach to Wave Equation Bilinear Estimates Revisit 波方程双线性估计的物理空间方法再探
IF 2.4 1区 数学
Annals of Pde Pub Date : 2024-06-18 DOI: 10.1007/s40818-024-00176-x
Sheng Wang, Yi Zhou
{"title":"Physical Space Approach to Wave Equation Bilinear Estimates Revisit","authors":"Sheng Wang,&nbsp;Yi Zhou","doi":"10.1007/s40818-024-00176-x","DOIUrl":"10.1007/s40818-024-00176-x","url":null,"abstract":"<div><p>In the paper by Klainerman, Rodnianski and Tao [7], they give a physical space proof to a classical result of Klainerman and Machedon [3] for the bilinear space-time estimates of null forms. In this paper, we shall give an alternative and very simple physical space proof of the same bilinear estimates by applying div-curl type lemma of Zhou [14] and Wang and Zhou [12, 13]. We have only attained the limited goal of proving the bilinear estimates for the dyadic piece of the solution. Summing up the dyadic parts leads to the bilinear estimates with a Besov loss. As far as we know, the later development of wave maps [1, 2, 8,9,10,11], and the proof of bounded curvature theorem [5, 6] rely on basic ideas of Klainerman and Machedon [3] as well as Klainerman, Rodnianski and Tao [7].</p></div>","PeriodicalId":36382,"journal":{"name":"Annals of Pde","volume":"10 2","pages":""},"PeriodicalIF":2.4,"publicationDate":"2024-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142412326","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
Correction: Ill-Posedness of the Two-Dimensional Stationary Navier–Stokes Equations on the Whole Plane 更正：全平面上的二维静态纳维-斯托克斯方程的假定性
IF 2.4 1区 数学
Annals of Pde Pub Date : 2024-06-18 DOI: 10.1007/s40818-024-00178-9
Mikihiro Fujii
{"title":"Correction: Ill-Posedness of the Two-Dimensional Stationary Navier–Stokes Equations on the Whole Plane","authors":"Mikihiro Fujii","doi":"10.1007/s40818-024-00178-9","DOIUrl":"10.1007/s40818-024-00178-9","url":null,"abstract":"","PeriodicalId":36382,"journal":{"name":"Annals of Pde","volume":"10 2","pages":""},"PeriodicalIF":2.4,"publicationDate":"2024-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142412334","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
Ill-Posedness of the Two-Dimensional Stationary Navier–Stokes Equations on the Whole Plane 全平面上的二维静态纳维-斯托克斯方程的假定性
IF 2.4 1区 数学
Annals of Pde Pub Date : 2024-05-28 DOI: 10.1007/s40818-024-00174-z
Mikihiro Fujii
{"title":"Ill-Posedness of the Two-Dimensional Stationary Navier–Stokes Equations on the Whole Plane","authors":"Mikihiro Fujii","doi":"10.1007/s40818-024-00174-z","DOIUrl":"10.1007/s40818-024-00174-z","url":null,"abstract":"<div><p>We consider the two-dimensional stationary Navier–Stokes equations on the whole plane <span>(mathbb {R}^2)</span>. In the higher-dimensional cases <span>(mathbb {R}^n)</span> with <span>(n geqslant 3)</span>, the well-posedness and ill-posedness in scaling critical spaces are well-investigated by numerous papers. However, the corresponding problem in the two-dimensional whole plane case has been known as an open problem due to inherent difficulties of two-dimensional analysis. The aim of this paper is to address this issue and solve it negatively. More precisely, we prove the ill-posedness in the scaling critical Besov spaces based on <span>(L^p(mathbb {R}^2))</span> for all <span>(1 leqslant p leqslant 2)</span> in the sense of the discontinuity of the solution map. To overcome the difficulties, we propose a new method based on the contradictory argument that reduces the problem to the analysis of the corresponding nonstationary Navier–Stokes equations and shows the existence of nonstationary solutions with strange large time behavior, if we suppose to contrary that the stationary problem is well-posed.</p></div>","PeriodicalId":36382,"journal":{"name":"Annals of Pde","volume":"10 1","pages":""},"PeriodicalIF":2.4,"publicationDate":"2024-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142414711","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
Kerr Stability in External Regions 外部区域的克尔稳定性
IF 2.4 1区 数学
Annals of Pde Pub Date : 2024-05-07 DOI: 10.1007/s40818-024-00173-0
Dawei Shen
{"title":"Kerr Stability in External Regions","authors":"Dawei Shen","doi":"10.1007/s40818-024-00173-0","DOIUrl":"10.1007/s40818-024-00173-0","url":null,"abstract":"<div><p>In 2003, Klainerman and Nicolò [14] proved the stability of Minkowski in the case of the exterior of an outgoing null cone. Relying on the method used in [14], Caciotta and Nicolò [2] proved the stability of Kerr spacetime in <i>external regions</i>, i.e. outside an outgoing null cone far away from the Kerr <i>event horizon</i>. In this paper, we give a new proof of [2]. Compared to [2], we reduce the number of derivatives needed in the proof, simplify the treatment of the last slice, and provide a unified treatment of the decay of initial data which contains in particular the initial data considered by Klainerman and Szeftel in [20]. Also, concerning the treatment of curvature estimates, similar to [25], we replace the vectorfield method used in [2, 14] by <span>(r^p)</span>–<i>weighted estimates</i> introduced by Dafermos and Rodnianski in [8].</p></div>","PeriodicalId":36382,"journal":{"name":"Annals of Pde","volume":"10 1","pages":""},"PeriodicalIF":2.4,"publicationDate":"2024-05-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141003974","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
Asymptotics and Convergence for the Complex Monge-Ampère Equation 复杂蒙日-安培方程的渐近性和收敛性
IF 2.4 1区 数学
Annals of Pde Pub Date : 2024-04-02 DOI: 10.1007/s40818-024-00171-2
Qing Han, Xumin Jiang
{"title":"Asymptotics and Convergence for the Complex Monge-Ampère Equation","authors":"Qing Han,&nbsp;Xumin Jiang","doi":"10.1007/s40818-024-00171-2","DOIUrl":"10.1007/s40818-024-00171-2","url":null,"abstract":"<div><p>We study the asymptotics of complete Kähler-Einstein metrics on strictly pseudoconvex domains in <span>(mathbb {C}^n)</span> and derive a convergence theorem for solutions to the corresponding Monge-Ampère equation. If only a portion of the boundary is analytic, the solutions satisfy Gevrey type estimates for tangential derivatives. A counterexample for the model linearized equation suggests that there is no local convergence theorem for the complex Monge-Ampère equation.</p></div>","PeriodicalId":36382,"journal":{"name":"Annals of Pde","volume":"10 1","pages":""},"PeriodicalIF":2.4,"publicationDate":"2024-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142409427","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
Generic Regularity of Level Set Flows with Spherical Singularity 具有球状奇异性的水平集流的一般规律性
IF 2.4 1区 数学
Annals of Pde Pub Date : 2024-03-29 DOI: 10.1007/s40818-024-00170-3
Ao Sun, Jinxin Xue
{"title":"Generic Regularity of Level Set Flows with Spherical Singularity","authors":"Ao Sun,&nbsp;Jinxin Xue","doi":"10.1007/s40818-024-00170-3","DOIUrl":"10.1007/s40818-024-00170-3","url":null,"abstract":"<div><p>The sphere is well-known as the only generic compact shrinker for mean curvature flow (MCF). In this paper, we characterize the generic dynamics of MCFs with a spherical singularity. In terms of the level set flow formulation of MCF, we establish that generically the arrival time function of level set flow with spherical singularity has at most <span>(C^2)</span> regularity.</p></div>","PeriodicalId":36382,"journal":{"name":"Annals of Pde","volume":"10 1","pages":""},"PeriodicalIF":2.4,"publicationDate":"2024-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140368117","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
Static Vacuum Extensions With Prescribed Bartnik Boundary Data Near a General Static Vacuum Metric 一般静态真空度附近具有规定巴特尼克边界数据的静态真空扩展
IF 2.4 1区 数学
Annals of Pde Pub Date : 2024-03-05 DOI: 10.1007/s40818-024-00169-w
Zhongshan An, Lan-Hsuan Huang
{"title":"Static Vacuum Extensions With Prescribed Bartnik Boundary Data Near a General Static Vacuum Metric","authors":"Zhongshan An,&nbsp;Lan-Hsuan Huang","doi":"10.1007/s40818-024-00169-w","DOIUrl":"10.1007/s40818-024-00169-w","url":null,"abstract":"<div><p>We introduce the notions of static regular of type (I) and type (II) and show that they are sufficient conditions for local well-posedness of solving asymptotically flat, static vacuum metrics with prescribed Bartnik boundary data. We then show that hypersurfaces in a very general open and dense family of hypersurfaces are static regular of type (II). As applications, we confirm Bartnik’s static vacuum extension conjecture for a large class of Bartnik boundary data, including those that can be far from Euclidean and have large ADM masses, and give many new examples of static vacuum metrics with intriguing geometry.</p></div>","PeriodicalId":36382,"journal":{"name":"Annals of Pde","volume":"10 1","pages":""},"PeriodicalIF":2.4,"publicationDate":"2024-03-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142410066","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
首页 上一页 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：481959085
Book学术官方微信