Annals of Pde最新文献

Optimal (C^{frac{1}{2}}) Regularity of the Boltzmann Equation in Non-Convex Domains 非凸域Boltzmann方程的最优(C^{frac{1}{2}})正则性

IF 2.6 1区数学

Annals of Pde Pub Date : 2026-05-06 DOI: 10.1007/s40818-026-00243-5

Gayoung An, Donghyun Lee

引用次数: 0

Linear Stability of the Slowly-Rotating Kerr-de Sitter Family 慢旋转Kerr-de Sitter族的线性稳定性

IF 2.6 1区数学

Annals of Pde Pub Date : 2026-04-30 DOI: 10.1007/s40818-026-00236-4

Allen Juntao Fang

{"title":"Linear Stability of the Slowly-Rotating Kerr-de Sitter Family","authors":"Allen Juntao Fang","doi":"10.1007/s40818-026-00236-4","DOIUrl":"10.1007/s40818-026-00236-4","url":null,"abstract":"<div><p>In this paper, we prove that the slowly-rotating Kerr-de Sitter family of black holes is linearly stable as a family of solutions to the Einstein vacuum equations with <span>(Lambda >0)</span> in harmonic (wave) gauge. This article is part of a series that provides a novel proof of the full nonlinear stability of the slowly-rotating Kerr-de Sitter family. This paper and its follow-up offer a self-contained alternative approach to nonlinear stability of the Kerr-de Sitter family from the original work of Hintz, Vasy Hintz and Vasy (Acta Math. <b>220</b>(1), 1–206 (2018a). https://doi.org/10.4310/ACTA.2018.v220.n1.a1) by interpreting quasinormal modes as <span>(H^k)</span> eigenvalues of an operator on a Hilbert space, and using integrated local energy decay estimates to prove the existence of a spectral gap. We also do not compactify the spacetime, thus avoiding the use of <i>b</i>-calculus and instead only use standard pseudo-differential arguments in a neighborhood of the trapped set; and avoid constraint damping altogether. The methods in the current paper offer an explicit example of how to use the vectorfield method to achieve resolvent estimates on a trapping background.</p></div>","PeriodicalId":36382,"journal":{"name":"Annals of Pde","volume":"12 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2026-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s40818-026-00236-4.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147797042","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

Modified Scattering for the Three Dimensional Maxwell-Dirac System 三维Maxwell-Dirac系统的修正散射

IF 2.6 1区数学

Annals of Pde Pub Date : 2026-04-22 DOI: 10.1007/s40818-026-00242-6

Sebastian Herr, Mihaela Ifrim, Martin Spitz

引用次数: 0

Failure of Calderón-Zygmund Estimates for the p-Laplace Equation p-拉普拉斯方程Calderón-Zygmund估计的失败

IF 2.6 1区数学

Annals of Pde Pub Date : 2026-04-02 DOI: 10.1007/s40818-026-00239-1

Armin Schikorra

引用次数: 0

Modified Scattering for the Cubic Schrödinger Equation on Diophantine Waveguides 丢番图波导上三次Schrödinger方程的修正散射

IF 2.6 1区数学

Annals of Pde Pub Date : 2026-03-21 DOI: 10.1007/s40818-026-00234-6

Nicolas Camps, Gigliola Staffilani

引用次数: 0

On the Well-Posedness of the KP-I Equation 关于KP-I方程的适定性

IF 2.6 1区数学

Annals of Pde Pub Date : 2026-03-16 DOI: 10.1007/s40818-026-00235-5

Zihua Guo, Luc Molinet

引用次数: 0

IF 2.6 1区数学

Annals of Pde Pub Date : 2026-03-06 DOI: 10.1007/s40818-026-00233-7

Feng Shao, Dongyi Wei, Zhifei Zhang

引用次数: 0

Massive Wave Propagation Near Null Infinity 零无穷大附近的大质量波传播

IF 2.6 1区数学

Annals of Pde Pub Date : 2026-03-05 DOI: 10.1007/s40818-026-00232-8

Ethan Sussman

{"title":"Massive Wave Propagation Near Null Infinity","authors":"Ethan Sussman","doi":"10.1007/s40818-026-00232-8","DOIUrl":"10.1007/s40818-026-00232-8","url":null,"abstract":"<div><p>We study, fully microlocally, the propagation of massive waves on the <i>octagonal compactification</i></p><div><div><span>$$begin{aligned} mathbb {O}=[overline{mathbb {R}^{1,d}};mathscr {I};1/2] end{aligned}$$</span></div></div><p>of asymptotically Minkowski spacetime, which allows a detailed analysis both at timelike and spacelike infinity (as previously investigated using Parenti–Shubin–Melrose’s sc-calculus) and, more novelly, at null infinity, denoted <span>(mathscr {I})</span>. The analysis is closely related to Hintz–Vasy’s recent analysis of massless wave propagation at null infinity using the “e,b-calculus” on <span>(mathbb {O})</span>. We prove several elementary corollaries regarding the Klein–Gordon IVP. Our main technical tool is a fully symbolic pseudodifferential calculus, <span>(Psi _{textrm{de,sc}}(mathbb {O}))</span>, the “de,sc-calculus” on <span>(mathbb {O})</span>. The ‘de’ refers to the structure (“double edge”) of the calculus at null infinity, and the ‘sc’ refers to the structure (“scattering”) at the other boundary faces. We relate this structure to the hyperbolic coordinates used in other studies of the Klein–Gordon equation. Unlike hyperbolic coordinates, the de,sc- boundary fibration structure is Poincaré invariant.\u0000</p></div>","PeriodicalId":36382,"journal":{"name":"Annals of Pde","volume":"12 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2026-03-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s40818-026-00232-8.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147362768","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

Low Regularity of Self-Similar Solutions of Two-Dimensional Riemann Problems with Shocks for the Isentropic Euler System 等熵欧拉系统含冲击的二维Riemann问题自相似解的低正则性

IF 2.6 1区数学

Annals of Pde Pub Date : 2026-03-02 DOI: 10.1007/s40818-025-00225-z

Gui-Qiang G. Chen, Mikhail Feldman, Wei Xiang

{"title":"Low Regularity of Self-Similar Solutions of Two-Dimensional Riemann Problems with Shocks for the Isentropic Euler System","authors":"Gui-Qiang G. Chen, Mikhail Feldman, Wei Xiang","doi":"10.1007/s40818-025-00225-z","DOIUrl":"10.1007/s40818-025-00225-z","url":null,"abstract":"<div>\u0000 \u0000 <p>We are concerned with the low regularity of self-similar solutions of two-dimensional Riemann problems for the isentropic Euler system. We establish a general framework for the analysis of the local regularity of such solutions for a class of two-dimensional Riemann problems for the isentropic Euler system, which includes the regular shock reflection problem, the Prandtl reflection problem, the Lighthill diffraction problem, and the four-shock Riemann problem. We prove that the velocity is not in <span>(H^1)</span> in the subsonic domain for the self-similar solutions of these problems in general. This indicates that the self-similar solutions of the Riemann problems with shocks for the isentropic Euler system are of much more complicated structure than those for the Euler system for potential flow; in particular, the velocity is not necessarily continuous in the subsonic domain. The proof is based on a regularization of the isentropic Euler system to derive the transport equation for the vorticity, a renormalization argument extended to the case of domains with boundary, and DiPerna-Lions-type commutator estimates.</p>\u0000 </div>","PeriodicalId":36382,"journal":{"name":"Annals of Pde","volume":"12 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2026-03-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s40818-025-00225-z.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147336264","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

Desingularization and Global Continuation for Hollow Vortices 空心涡旋的非奇异化与全局延拓

IF 2.6 1区数学

Annals of Pde Pub Date : 2026-02-26 DOI: 10.1007/s40818-025-00229-9

Robin Ming Chen, Samuel Walsh, Miles H. Wheeler

引用次数: 0