Annals of Pde最新文献_第4页

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

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

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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

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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

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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

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A Fully Nonlinear Degenerate Free Transmission Problem 全非线性退化自由传输问题

IF 2.4 1区数学

Annals of Pde Pub Date : 2024-02-20 DOI: 10.1007/s40818-024-00168-x

Gerardo Huaroto, Edgard A. Pimentel, Giane C. Rampasso, Andrzej Święch

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Existence and Regularity for Prescribed Lorentzian Mean Curvature Hypersurfaces, and the Born–Infeld Model 规定洛伦兹平均曲率超曲面的存在性和正则性，以及玻恩-英菲尔德模型

IF 2.4 1区数学

Annals of Pde Pub Date : 2024-01-29 DOI: 10.1007/s40818-023-00167-4

Jaeyoung Byeon, Norihisa Ikoma, Andrea Malchiodi, Luciano Mari

{"title":"Existence and Regularity for Prescribed Lorentzian Mean Curvature Hypersurfaces, and the Born–Infeld Model","authors":"Jaeyoung Byeon, Norihisa Ikoma, Andrea Malchiodi, Luciano Mari","doi":"10.1007/s40818-023-00167-4","DOIUrl":"10.1007/s40818-023-00167-4","url":null,"abstract":"<div><p>Given a measure <span>(rho )</span> on a domain <span>(Omega subset {mathbb {R}}^m)</span>, we study spacelike graphs over <span>(Omega )</span> in Minkowski space with Lorentzian mean curvature <span>(rho )</span> and Dirichlet boundary condition on <span>(partial Omega )</span>, which solve </p><div><figure><div><div><picture><img></picture></div></div></figure></div><p> The graph function also represents the electric potential generated by a charge <span>(rho )</span> in electrostatic Born-Infeld’s theory. Even though there exists a unique minimizer <span>(u_rho )</span> of the associated action </p><div><div><span>$$begin{aligned} I_rho (psi ) doteq int _{Omega } Big ( 1 - sqrt{1-|Dpsi |^2} Big ) textrm{d}x - langle rho , psi rangle end{aligned}$$</span></div></div><p>among functions <span>(psi )</span> satisfying <span>(|Dpsi | le 1)</span>, by the lack of smoothness of the Lagrangian density for <span>(|Dpsi | = 1)</span> one cannot guarantee that <span>(u_rho )</span> satisfies the Euler-Lagrange equation (<span>(mathcal{B}mathcal{I})</span>). A chief difficulty comes from the possible presence of light segments in the graph of <span>(u_rho )</span>. In this paper, we investigate the existence of a solution for general <span>(rho )</span>. In particular, we give sufficient conditions to guarantee that <span>(u_rho )</span> solves (<span>(mathcal{B}mathcal{I})</span>) and enjoys <span>(log )</span>-improved energy and <span>(W^{2,2}_textrm{loc})</span> estimate. Furthermore, we construct examples which suggest a sharp threshold for the regularity of <span>(rho )</span> to ensure the solvability of (<span>(mathcal{B}mathcal{I})</span>).</p></div>","PeriodicalId":36382,"journal":{"name":"Annals of Pde","volume":"10 1","pages":""},"PeriodicalIF":2.4,"publicationDate":"2024-01-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142414915","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

Global existence for perturbations of the 2D stochastic Navier–Stokes equations with space-time white noise 带有时空白噪声的二维随机纳维-斯托克斯方程扰动的全局存在性

IF 2.8 1区数学

Annals of Pde Pub Date : 2023-12-27 DOI: 10.1007/s40818-023-00165-6

Martin Hairer, Tommaso Rosati

{"title":"Global existence for perturbations of the 2D stochastic Navier–Stokes equations with space-time white noise","authors":"Martin Hairer, Tommaso Rosati","doi":"10.1007/s40818-023-00165-6","DOIUrl":"10.1007/s40818-023-00165-6","url":null,"abstract":"<div><p>We prove global in time well-posedness for perturbations of the 2D stochastic Navier–Stokes equations </p><div><div><span>$$begin{aligned} partial _t u + u cdot nabla u= & {} Delta u - nabla p + zeta + xi ;, qquad u (0, cdot ) = u_{0} ;, {text {div}}(u)= & {} 0 ;, end{aligned}$$</span></div></div><p>driven by additive space-time white noise <span>( xi )</span>, with perturbation <span>( zeta )</span> in the Hölder–Besov space <span>(mathcal {C}^{-2 + 3kappa } )</span>, periodic boundary conditions and initial condition <span>( u_{0} in mathcal {C}^{-1 + kappa } )</span> for any <span>( kappa >0 )</span>. The proof relies on an energy estimate which in turn builds on a dynamic high-low frequency decomposition and tools from paracontrolled calculus. Our argument uses that the solution to the linear equation is a <span>( log )</span>–correlated field, yielding a double exponential growth bound on the solution. Notably, our method does not rely on any explicit knowledge of the invariant measure to the SPDE, hence the perturbation <span>( zeta )</span> is not restricted to the Cameron–Martin space of the noise, and the initial condition may be anticipative. Finally, we introduce a notion of weak solution that leads to well-posedness for all initial data <span>( u_{0})</span> in <span>( L^{2} )</span>, the critical space of initial conditions.</p></div>","PeriodicalId":36382,"journal":{"name":"Annals of Pde","volume":"10 1","pages":""},"PeriodicalIF":2.8,"publicationDate":"2023-12-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s40818-023-00165-6.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139050689","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

Nonlinear Landau Damping for the Vlasov–Poisson System in (mathbb {R}^3): The Poisson Equilibrium (mathbb {R}^3) 中弗拉索夫-泊松系统的非线性朗道阻尼：泊松均衡

IF 2.8 1区数学

Annals of Pde Pub Date : 2023-12-13 DOI: 10.1007/s40818-023-00161-w

Alexandru D. Ionescu, Benoit Pausader, Xuecheng Wang, Klaus Widmayer

引用次数: 0

Time Periodic Solutions Close to Localized Radial Monotone Profiles for the 2D Euler Equations 接近二维欧拉方程局部径向单调剖面的时间周期解

IF 2.8 1区数学

Annals of Pde Pub Date : 2023-12-12 DOI: 10.1007/s40818-023-00166-5

Claudia García, Taoufik Hmidi, Joan Mateu

{"title":"Time Periodic Solutions Close to Localized Radial Monotone Profiles for the 2D Euler Equations","authors":"Claudia García, Taoufik Hmidi, Joan Mateu","doi":"10.1007/s40818-023-00166-5","DOIUrl":"10.1007/s40818-023-00166-5","url":null,"abstract":"<div><p>In this paper, we address for the 2D Euler equations the existence of rigid time periodic solutions close to stationary radial vortices of type <span>(f_0(|x|)textbf{1}_{{{,mathrm{mathbb {D}},}}}(x))</span>, with <span>({{,mathrm{mathbb {D}},}})</span> the unit disc and <span>(f_0)</span> being a strictly monotonic profile with constant sign. We distinguish two scenarios according to the sign of the profile: <i>defocusing and focusing.</i> In the first regime, we have scarcity of the bifurcating curves associated with lower symmetry. However in the <i>focusing case</i> we get a countable family of bifurcating solutions associated with large symmetry. The approach developed in this work is new and flexible, and the explicit expression of the radial profile is no longer required as in [41] with the quadratic shape. The alternative for that is a refined study of the associated spectral problem based on Sturm-Liouville differential equation with a variable potential that changes the sign depending on the shape of the profile and the location of the time period. Deep hidden structure on positive definiteness of some intermediate integral operators are also discovered and used in a crucial way. Notice that a special study will be performed for the linear problem associated with the first mode founded on Prüfer transformation and Kneser’s Theorem on the non-oscillation phenomenon.</p></div>","PeriodicalId":36382,"journal":{"name":"Annals of Pde","volume":"10 1","pages":""},"PeriodicalIF":2.8,"publicationDate":"2023-12-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138822346","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