Annals of Pde最新文献_第8页

The Case Against Smooth Null Infinity III: Early-Time Asymptotics for Higher (ell )-Modes of Linear Waves on a Schwarzschild Background 反对光滑零无穷大的情形III：Schwarzschild背景下线性波的高（ell）模的早期渐近

IF 2.8 1区数学

Annals of Pde Pub Date : 2022-06-07 DOI: 10.1007/s40818-022-00129-2

Leonhard M. A. Kehrberger

{"title":"The Case Against Smooth Null Infinity III: Early-Time Asymptotics for Higher (ell )-Modes of Linear Waves on a Schwarzschild Background","authors":"Leonhard M. A. Kehrberger","doi":"10.1007/s40818-022-00129-2","DOIUrl":"10.1007/s40818-022-00129-2","url":null,"abstract":"<div>In this paper, we derive the early-time asymptotics for fixed-frequency solutions (phi _ell ) to the wave equation (Box _g phi _ell =0) on a fixed Schwarzschild background ((M>0)) arising from the no incoming radiation condition on ({mathscr {I}}^-) and polynomially decaying data, (rphi _ell sim t^{-1}) as (trightarrow -infty ), on either a timelike boundary of constant area radius (r>2M) (I) or an ingoing null hypersurface (II). In case (I), we show that the asymptotic expansion of (partial _v(rphi _ell )) along outgoing null hypersurfaces near spacelike infinity (i^0) contains logarithmic terms at order (r^{-3-ell }log r). In contrast, in case (II), we obtain that the asymptotic expansion of (partial _v(rphi _ell )) near spacelike infinity (i^0) contains logarithmic terms already at order (r^{-3}log r) (unless (ell =1)). These results suggest an alternative approach to the study of late-time asymptotics near future timelike infinity (i^+) that does not assume conformally smooth or compactly supported Cauchy data: In case (I), our results indicate a logarithmically modified Price’s law for each (ell )-mode. On the other hand, the data of case (II) lead to much stronger deviations from Price’s law. In particular, we conjecture that compactly supported scattering data on ({mathscr {H}}^-) and ({mathscr {I}}^-) lead to solutions that exhibit the same late-time asymptotics on ({mathscr {I}}^+) for each (ell ): (rphi _ell |_{{mathscr {I}}^+}sim u^{-2}) as (urightarrow infty ).</div>","PeriodicalId":36382,"journal":{"name":"Annals of Pde","volume":"8 2","pages":""},"PeriodicalIF":2.8,"publicationDate":"2022-06-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s40818-022-00129-2.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50459484","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: 7

Quantitative Derivation and Scattering of the 3D Cubic NLS in the Energy Space 三维三次NLS在能量空间中的定量推导和散射

IF 2.8 1区数学

Annals of Pde Pub Date : 2022-05-27 DOI: 10.1007/s40818-022-00126-5

Xuwen Chen, Justin Holmer

引用次数: 7

Global Entropy Solutions and Newtonian Limit for the Relativistic Euler Equations 相对论Euler方程的全局熵解和牛顿极限

IF 2.8 1区数学

Annals of Pde Pub Date : 2022-05-12 DOI: 10.1007/s40818-022-00123-8

Gui-Qiang G. Chen, Matthew R. I. Schrecker

引用次数: 0

Decay of the Weyl curvature in expanding black hole cosmologies 膨胀黑洞宇宙学中Weyl曲率的衰变

IF 2.8 1区数学

Annals of Pde Pub Date : 2022-05-04 DOI: 10.1007/s40818-022-00125-6

Volker Schlue

引用次数: 10

A global method for deterministic and stochastic homogenisation in BV BV中确定性和随机均匀化的一种全局方法

IF 2.8 1区数学

Annals of Pde Pub Date : 2022-04-07 DOI: 10.1007/s40818-022-00119-4

Filippo Cagnetti, Gianni Dal Maso, Lucia Scardia, Caterina Ida Zeppieri

引用次数: 5

Localized Mixing Zone for Muskat Bubbles and Turned Interfaces Muscat气泡和翻转界面的局部混合区

IF 2.8 1区数学

Annals of Pde Pub Date : 2022-04-07 DOI: 10.1007/s40818-022-00121-w

Á. Castro, D. Faraco, F. Mengual

引用次数: 8

SO(2) Symmetry of the Translating Solitons of the Mean Curvature Flow in (mathbb {R}^4) （mathbb｛R｝^4）中平均曲率流平移孤立子的SO（2）对称性

IF 2.8 1区数学

Annals of Pde Pub Date : 2022-03-25 DOI: 10.1007/s40818-022-00120-x

Jingze Zhu

引用次数: 1

Spectral Analysis for Singularity Formation of the Two Dimensional Keller–Segel System 二维Keller-Segel系统奇异性形成的谱分析

IF 2.8 1区数学

Annals of Pde Pub Date : 2022-03-19 DOI: 10.1007/s40818-022-00118-5

Charles Collot, Tej-Eddine Ghoul, Nader Masmoudi, Van Tien Nguyen

引用次数: 9

From Vlasov-Maxwell-Boltzmann system to two-fluid incompressible Navier-Stokes-Fourier-Maxwell system with Ohm’s law: convergence for classical solutions 从Vlasov-Maxwell-Boltzmann系统到具有欧姆定律的二流体不可压缩Navier-Stokes傅立叶-Maxwell系统：经典解的收敛性

IF 2.8 1区数学

Annals of Pde Pub Date : 2022-02-13 DOI: 10.1007/s40818-022-00117-6

Ning Jiang, Yi-Long Luo

{"title":"From Vlasov-Maxwell-Boltzmann system to two-fluid incompressible Navier-Stokes-Fourier-Maxwell system with Ohm’s law: convergence for classical solutions","authors":"Ning Jiang, Yi-Long Luo","doi":"10.1007/s40818-022-00117-6","DOIUrl":"10.1007/s40818-022-00117-6","url":null,"abstract":"<div>We consider the two-species Vlasov-Maxwell-Boltzmann (VMB) system with the scaling under which the moments of the fluctuations to the global Maxwellians formally converge to two-fluid incompressible Navier-Stokes-Fourier-Maxwell (NSFM) system with Ohm’s law. We prove the uniform estimates with respect to Knudsen number (varepsilon ) for the fluctuations by employing two types of micro-macro decompositions, and furthermore a hidden damping effect from the microscopic Ohm’s law. As consequences, the existence of the global-in-time classical solutions of VMB with all (varepsilon in (0,1]) is established. Moreover, the convergence of the fluctuations of the solutions of VMB to the classical solutions of NSFM with Ohm’s law is rigorously justified. This limit was justified in the recent breakthrough of Arsénio and Saint-Raymond (From the Vlasov-Maxwell-Boltzmann system to incompressible viscous electro-magneto-hydrodynamics. Vol. 1. EMS Monographs in Mathematics, European Mathematical Society (EMS), Zürich, 2019) from renormalized solutions of VMB to dissipative solutions of incompressible viscous electro-magneto-hydrodynamics under the suitable scalings. In this sense, our result provides a classical solution analogue of the corresponding limit in Arsénio and Saint-Raymond (From the Vlasov-Maxwell-Boltzmann system to incompressible viscous electro-magneto-hydrodynamics. Vol. 1. EMS Monographs in Mathematics, European Mathematical Society (EMS), Zürich, 2019) .</div>","PeriodicalId":36382,"journal":{"name":"Annals of Pde","volume":"8 1","pages":""},"PeriodicalIF":2.8,"publicationDate":"2022-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50477036","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: 15

A Scale-Critical Trapped Surface Formation Criterion: A New Proof Via Signature for Decay Rates 尺度临界陷阱表面形成准则：衰变率特征的新证明

IF 2.8 1区数学

Annals of Pde Pub Date : 2022-01-16 DOI: 10.1007/s40818-021-00114-1

Xinliang An

引用次数: 6