Annals of Pde最新文献_第5页

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

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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

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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

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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