Annals of PDE偏微分方程年刊
Annals of PDE(英文缩写 ANN PDE),ISSN 2524-5317,eISSN 2199-2576,中文译名:偏微分方程年刊 是一本学术期刊。本页汇总该期刊的最新影响因子、分区信息以及最新收录于 PubMed 的文献,帮助您快速了解期刊全貌。
发文量统计区间：2025-10-01 至 2026-09-30，按本站收录文献的发表日期统计。
期刊介绍
历年影响因子趋势
| JCR 数据年份 | 影响因子 | JCR 分区 |
|---|---|---|
| 2021 | 2.697 | Q1 |
| 2022 | 2.800 | Q1 |
| 2023 | 2.400 | Q1 |
| 2024 | 2.600 | Q1 |
| 2025 | 3.000 | Q1 |
Annals of PDE 最新收录文献
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1. Improved Moduli of Continuity for Degenerate Phase Transitions.
PMID:日期:2026-09-05We substantially improve in two scenarios the current state-of-the-art modulus of continuity for weak solutions to the dimensional, two-phase Stefan problem featuring a degenerate diffusion: for , we sharpen it to for , we derive an unexpected Hölder modulus.
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2. Stability in Quasineutral Plasmas with Thermalized Electrons.
PMID:日期:2026-07-21We 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.
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3. Existence of Finite Time Blow-Up in Keller-Segel System.
PMID:日期:2026-05-16Perhaps the most classical diffusion model for chemotaxis is the Keller-Segel system We show that there exists such that for any satisfying and any given points in there is an initial data of ( ) for which the solution (, ) blows up in finite time as with the approximate profile with where is the Euler-Mascheroni constant, and such that This construction generalizes the existence result of the stable blow-up dynamics recently proved in [17, 18].
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4. Linear Stability of the Slowly-Rotating Kerr-de Sitter Family.
PMID:日期:2026-04-30In 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 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. (1), 1-206 (2018a). 10.4310/ACTA.2018.v220.n1.a1) by interpreting quasinormal modes as 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 -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.
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5. Anomalous Dissipation and Lack of Selection in the Obukhov-Corrsin Theory of Scalar Turbulence.
PMID:日期:2023-11-02The Obukhov-Corrsin theory of scalar turbulence [21, 54] advances quantitative predictions on passive-scalar advection in a turbulent regime and can be regarded as the analogue for passive scalars of Kolmogorov's K41 theory of fully developed turbulence [47]. The scaling analysis of Obukhov and Corrsin from 1949 to 1951 identifies a critical regularity threshold for the advection-diffusion equation and predicts anomalous dissipation in the limit of vanishing diffusivity in the supercritical regime. In this paper we provide a fully rigorous mathematical validation of this prediction by constructing a velocity field and an initial datum such that the unique bounded solution of the advection-diffusion equation is bounded uniformly-in-diffusivity within any fixed supercritical Obukhov-Corrsin regularity regime while also exhibiting anomalous dissipation. Our approach relies on a fine quantitative analysis of the interaction between the spatial scale of the solution and the scale of the Brownian motion which represents diffusion in a stochastic Lagrangian setting. This provides a direct Lagrangian approach to anomalous dissipation which is fundamental in order to get detailed insight on the behavior of the solution. Exploiting further this approach, we also show that for a velocity field in of space and time (for an arbitrary ) neither vanishing diffusivity nor regularization by convolution provide a selection criterion for bounded solutions of the advection equation. This is motivated by the fundamental open problem of the selection of solutions of the Euler equations as vanishing-viscosity limit of solutions of the Navier-Stokes equations and provides a complete negative answer in the case of passive advection.
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6. Naked Singularities in the Einstein-Euler System.
6. 爱因斯坦-欧拉系统中的裸奇点PMID:日期:2023-02-07In 1990, based on numerical and formal asymptotic analysis, Ori and Piran predicted the existence of selfsimilar spacetimes, called relativistic Larson-Penston solutions, that can be suitably flattened to obtain examples of spacetimes that dynamically form naked singularities from smooth initial data, and solve the radially symmetric Einstein-Euler system. Despite its importance, a rigorous proof of the existence of such spacetimes has remained elusive, in part due to the complications associated with the analysis across the so-called sonic hypersurface. We provide a rigorous mathematical proof. Our strategy is based on a delicate study of nonlinear invariances associated with the underlying non-autonomous dynamical system to which the problem reduces after a selfsimilar reduction. Key technical ingredients are a monotonicity lemma tailored to the problem, an ad hoc shooting method developed to construct a solution connecting the sonic hypersurface to the so-called Friedmann solution, and a nonlinear argument to construct the maximal analytic extension of the solution. Finally, we reformulate the problem in double-null gauge to flatten the selfsimilar profile and thus obtain an asymptotically flat spacetime with an isolated naked singularity.
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7. Uniqueness of Solutions to Nonlinear Schrödinger Equations from their Zeros.
PMID:日期:2022-09-14We show novel types of uniqueness and rigidity results for Schrödinger equations in either the nonlinear case or in the presence of a complex-valued potential. As our main result we obtain that the trivial solution is the only solution for which the assumptions hold, where are certain subsets of codimension one. In particular, is for dimension . Our main theorem can be seen as a nonlinear analogue of discrete Fourier uniqueness pairs such as the celebrated Radchenko-Viazovska formula in [21], and the uniqueness result of the second author and M. Sousa for powers of integers [22]. As an additional application, we deduce rigidity results for solutions to some semilinear elliptic equations from their zeros.
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8. Decay of the Weyl curvature in expanding black hole cosmologies.
PMID:日期:2022-05-04This paper is motivated by the non-linear stability problem for the expanding region of Kerr de Sitter cosmologies in the context of Einstein's equations with positive cosmological constant. We show that under dynamically realistic assumptions the conformal Weyl curvature of the spacetime decays towards future null infinity. More precisely we establish decay estimates for Weyl fields which are (i) uniform (with respect to a global time function) (ii) optimal (with respect to the rate) and (iii) consistent with a global existence proof (in terms of regularity). The proof relies on a geometric positivity property of compatible currents which is a manifestation of the global redshift effect capturing the expansion of the spacetime.
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9. {"_":"A global method for deterministic and stochastic homogenisation in .","i":["BV"]}
PMID:日期:2022-04-07In this paper we study the deterministic and stochastic homogenisation of free-discontinuity functionals under growth and coercivity conditions. The main novelty of our deterministic result is that we work under very general assumptions on the integrands which, in particular, are not required to be periodic in the space variable. Combining this result with the pointwise Subadditive Ergodic Theorem by Akcoglu and Krengel, we prove a stochastic homogenisation result, in the case of stationary random integrands. In particular, we characterise the limit integrands in terms of asymptotic cell formulas, as in the classical case of periodic homogenisation.
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10. Estimate on the Dimension of the Singular Set of the Supercritical Surface Quasigeostrophic Equation.
PMID:日期:2021-03-26We consider the SQG equation with dissipation given by a fractional Laplacian of order . We introduce a notion of suitable weak solution, which exists for every initial datum, and we prove that for such solution the singular set is contained in a compact set in spacetime of Hausdorff dimension at most .