Annals of Pde最新文献_第2页

Stability in Quasineutral Plasmas with Thermalized Electrons 具有热化电子的准中性等离子体的稳定性。

IF 3 1区数学

Annals of Pde Pub Date : 2026-07-21 DOI: 10.1007/s40818-026-00248-0

Megan Griffin-Pickering, Mikaela Iacobelli

{"title":"Stability in Quasineutral Plasmas with Thermalized Electrons","authors":"Megan Griffin-Pickering, Mikaela Iacobelli","doi":"10.1007/s40818-026-00248-0","DOIUrl":"10.1007/s40818-026-00248-0","url":null,"abstract":"<div><p>We study the quasineutral limit for the ionic Vlasov–Poisson system with thermalized electrons (VPME) on the torus in dimensions one to three, for rough solutions with bounded spatial density. Our main result is a quantitative stability theorem showing that quasineutral convergence is robust under exponentially small perturbations of the initial data, as measured in Wasserstein distance: given a regular family of reference solutions for which the quasineutral limit is known to hold, we prove that the same limit remains valid for perturbed solutions on the same time interval. The proof combines a kinetic-Wasserstein stability framework with a refined analysis of the Poisson–Boltzmann coupling specific to VPME. A central new ingredient is an improved control of the characteristic flow: we obtain quantitative bounds on the growth of characteristics in the velocity coordinate, with only polynomial deterioration in the Debye length. This yields new locally-uniform-in-time bounds on the spatial density and provides the key input needed to complete the stability estimates. These results bring the stability theory for the ionic model in the quasineutral regime close to the known instability threshold and substantially relax the smallness conditions required in earlier works. As a byproduct, our approach improves the moment assumptions in the global well-posedness theory for bounded-density solutions to VPME on the torus.\u0000</p></div>","PeriodicalId":36382,"journal":{"name":"Annals of Pde","volume":"12 2","pages":""},"PeriodicalIF":3.0,"publicationDate":"2026-07-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC13388360/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148563091","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

Infinite Time Bubbling for the SU(2) Yang-Mills Heat Flow on (mathbb {R}^4) SU(2) Yang-Mills热流的无限时间鼓泡 (mathbb {R}^4)

IF 3 1区数学

Annals of Pde Pub Date : 2026-07-21 DOI: 10.1007/s40818-026-00244-4

Yannick Sire, Juncheng Wei, Youquan Zheng

引用次数: 0

On the Three-Dimensional Nernst-Planck-Boussinesq System 论三维能斯特-普朗克-布辛尼斯克系统

IF 3 1区数学

Annals of Pde Pub Date : 2026-07-20 DOI: 10.1007/s40818-026-00240-8

Elie Abdo, Ruimeng Hu, Quyuan Lin

引用次数: 0

Asymptotic Analysis of Harmonic Maps with Prescribed Singularities 具有规定奇异点调和映射的渐近分析

IF 3 1区数学

Annals of Pde Pub Date : 2026-07-15 DOI: 10.1007/s40818-026-00247-1

Qing Han, Marcus Khuri, Gilbert Weinstein, Jingang Xiong

{"title":"Asymptotic Analysis of Harmonic Maps with Prescribed Singularities","authors":"Qing Han, Marcus Khuri, Gilbert Weinstein, Jingang Xiong","doi":"10.1007/s40818-026-00247-1","DOIUrl":"10.1007/s40818-026-00247-1","url":null,"abstract":"<div><p>This is the first in a series of two papers to establish the mass-angular momentum inequality for multiple black holes. We study singular harmonic maps from domains of 3-dimensional Euclidean space to the hyperbolic plane having bounded hyperbolic distance to extreme Kerr harmonic maps. We prove that every such harmonic map admits a unique tangent harmonic map at the extreme black hole horizon. The possible tangent maps are classified and shown to be shifted ‘extreme Kerr’ geodesics in the hyperbolic plane that depend on two parameters, one determined by angular momentum and another by conical singularities. In addition, rates of convergence to the tangent map are established. Similarly, expansions in the asymptotically flat end are presented. These results, together with those of Li-Tian [24, 25] and Weinstein [35, 36], provide a complete regularity theory for harmonic maps from <span>(mathbb {R}^3setminus ztext {-axis})</span> to <span>(mathbb {H}^2)</span> with these prescribed singularities. The analysis is additionally utilized to prove existence of the so called near horizon limit, and to compute the associated near horizon geometries of extreme black holes.\u0000</p></div>","PeriodicalId":36382,"journal":{"name":"Annals of Pde","volume":"12 2","pages":""},"PeriodicalIF":3.0,"publicationDate":"2026-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s40818-026-00247-1.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148465938","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

A Free Boundary Problem for an Immersed Filament in 3D Stokes Flow 三维斯托克斯流中浸没细丝的自由边界问题

IF 3 1区数学

Annals of Pde Pub Date : 2026-07-13 DOI: 10.1007/s40818-026-00237-3

Laurel Ohm

引用次数: 0

Global Well-Posedness of the Energy-Critical Nonlinear Schrödinger Equations on (mathbb {T}^{d}) 能量临界非线性Schrödinger方程的全局适定性 (mathbb {T}^{d})

IF 3 1区数学

Annals of Pde Pub Date : 2026-07-13 DOI: 10.1007/s40818-026-00246-2

Beomjong Kwak

引用次数: 0

Self-similar Imploding Solutions of the Relativistic Euler Equations 相对论欧拉方程的自相似内爆解

IF 3 1区数学

Annals of Pde Pub Date : 2026-07-01 DOI: 10.1007/s40818-026-00245-3

Feng Shao, Dongyi Wei, Zhifei Zhang

{"title":"Self-similar Imploding Solutions of the Relativistic Euler Equations","authors":"Feng Shao, Dongyi Wei, Zhifei Zhang","doi":"10.1007/s40818-026-00245-3","DOIUrl":"10.1007/s40818-026-00245-3","url":null,"abstract":"<div><p>In their recent breakthrough works [<i>Ann. of Math. (2)</i>, <b>196</b> (2022), 567–778; <i>Invent. Math.</i>, <b>227</b> (2022), 247–413], Merle, Raphaël, Rodnianski, and Szeftel constructed finite-time blow-up solutions to energy supercritical defocusing nonlinear Schrödinger equations, with the leading order given by imploding solutions to isentropic compressible Euler equations. Motivated by these results, in this paper and its sequel [Shao, Wei and Zhang, <i>Forum Math. Pi</i>, <b>13</b> (2025), Paper No. e15, 59 pp], we find a new connection between supercritical defocusing nonlinear wave equations (NLW) and the isentropic relativistic Euler equations. More precisely, in this paper, we construct self-similar smooth imploding solutions of the isentropic relativistic Euler equations with an isothermal equation of state <span>(p=frac{1}{ell }varrho )</span> for <i>all</i> <span>(ell >1)</span> in physical space dimensions <span>(d=2,3)</span> and for <span>(ell >1)</span> close to 1 in higher dimensions. In our companion paper, we construct finite-time blow-up solutions for the complex-valued supercritical defocusing nonlinear wave equation, with the leading-order dynamics governed by the imploding solutions to the isentropic relativistic Euler equations constructed in the present paper.</p></div>","PeriodicalId":36382,"journal":{"name":"Annals of Pde","volume":"12 2","pages":""},"PeriodicalIF":3.0,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148349749","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

Existence of Finite Time Blow-Up in Keller-Segel System Keller-Segel系统有限时间爆破的存在性

IF 2.6 1区数学

Annals of Pde Pub Date : 2026-05-16 DOI: 10.1007/s40818-026-00241-7

Federico Buseghin, Juan Dávila, Manuel del Pino, Monica Musso

{"title":"Existence of Finite Time Blow-Up in Keller-Segel System","authors":"Federico Buseghin, Juan Dávila, Manuel del Pino, Monica Musso","doi":"10.1007/s40818-026-00241-7","DOIUrl":"10.1007/s40818-026-00241-7","url":null,"abstract":"<div><p>Perhaps the most classical diffusion model for chemotaxis is the Keller-Segel system </p><div><div><span>$$begin{aligned} left{ begin{aligned} u_t =&; Delta u - nabla cdot (u nabla v) quad {quad hbox {in } }mathbb {R}^2times (0,T), v =&; (-Delta _{mathbb {R}^2})^{-1} u := frac{1}{2pi } int _{mathbb {R}^2} log frac{1}{|x-z|},u(z,t) dz,&quad u(cdot ,0) = u_0^{star } ge 0quad text {in } mathbb {R}^2. end{aligned} right. end{aligned}$$</span></div><div>\u0000 (*)\u0000 </div></div><p>We show that there exists <span>(varepsilon >0)</span> such that for any <i>m</i> satisfying </p><div><div><span>$$begin{aligned} 8pi <mle 8pi +varepsilon end{aligned}$$</span></div></div><p>and any <i>k</i> given points <span>(q_{1},...,q_{k})</span> in <span>(mathbb {R}^{2})</span> there is an initial data <span>(u_0^*)</span> of (<span>(*)</span>) for which the solution <i>u</i>(<i>x</i>, <i>t</i>) blows up in finite time as <span>(trightarrow T)</span> with the approximate profile </p><div><div><span>$$ u(x,t)=sum _{j=1}^{k}frac{1}{lambda _{j}^{2}(t)}Uleft( frac{x-xi _{j}(t)}{lambda _{j}(t)}right) (1+o(1)), quad U(y)=frac{8}{(1+|y|^{2})^{2}}, $$</span></div></div><p>with <span>(lambda _{j}(t) approx 2e^{-frac{gamma +2}{2}}sqrt{T-t}e^{-sqrt{frac{|ln (T-t)|}{2}}} )</span> where <span>(gamma =0.57721...)</span> is the Euler-Mascheroni constant, <span>(xi _{j}(t)rightarrow q_{j}in mathbb {R}^{2})</span> and such that </p><div><div><span>$$ int _{mathbb {R}^2}u(x,t)dx=km. $$</span></div></div><p>This construction generalizes the existence result of the stable blow-up dynamics recently proved in [17, 18].</p></div>","PeriodicalId":36382,"journal":{"name":"Annals of Pde","volume":"12 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2026-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s40818-026-00241-7.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147938885","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

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