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On the uniqueness of weak solutions to the 3d Navier–Stokes equations in Vishik-type spaces vishik型空间中三维Navier-Stokes方程弱解的唯一性

IF 2.8 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics Letters

Pub Date : 2026-03-01 Epub Date: 2025-11-19 DOI: 10.1016/j.aml.2025.109826

Fan Wu

We revisit the classical problem of uniqueness of Leray–Hopf weak solutions to the three-dimensional incompressible Navier–Stokes equations. In the pioneering works, uniqueness was established under Prodi–Serrin type conditions, and later improved to critical Besov spaces [Chen–Miao–Zhang, Ann. Inst. H. Poincaré Anal. Non Linéaire 26(2009) 2165-2180]. A key step in Chen–Miao–Zhang’s result is the decomposition of the velocity field into a Lipschitz low-frequency part and a higher integrability high-frequency part. In this paper, we refine this approach by replacing the Lipschitz control with a sharper bound in the nonhomogeneous Besov space

B_{\infty, 1}^{1}

, using the framework of nonhomogeneous Vishik-type spaces. We establish an improved uniqueness criterion in Vishik-type spaces

V_{p, q, θ}^{r}

, which strictly extends the scope of classical Besov spaces used in prior works.

我们重新研究了三维不可压缩Navier-Stokes方程的Leray-Hopf弱解的唯一性问题。在开创性的著作中，在Prodi-Serrin型条件下建立了唯一性，后来又改进到临界Besov空间[陈淼张，Ann]。H.庞卡罗埃尔研究所。林氏学报26(2009)2165-2180。陈淼张结果的关键一步是将速度场分解为Lipschitz低频部分和高可积性的高频部分。在本文中，我们利用非齐次vishik型空间的框架，在非齐次Besov空间B∞，11中将Lipschitz控制替换为更锐利的界，从而改进了该方法。我们在vishik型空间Vp，q，θr中建立了一个改进的唯一性判据，严格地扩展了前人所使用的经典Besov空间的范围。

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引用次数: 0

Global stability for an advection–diffusion SI epidemic model with spatial heterogeneity in the critical case 临界情况下具有空间异质性的平流扩散SI流行病模型的全局稳定性

IF 2.8 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics Letters

Pub Date : 2026-03-01 Epub Date: 2025-11-20 DOI: 10.1016/j.aml.2025.109828

Jianpeng Wang , Kai Wang , Lei Wang , Zhidong Teng

In this paper, we are concerned with the global stability of disease-free steady state for a reaction–advection–diffusion SI epidemic model with heterogeneous diffusion and different advection when basic reproduction number

R_{0} = 1

. Furthermore, we also establish the criteria for the global stability of exponential positive steady state.

本文研究了具有非均匀扩散和不同平流的反应-平流-扩散SI流行病模型在基本繁殖数R0=1时无病稳态的全局稳定性问题。此外，我们还建立了指数正稳态全局稳定的判据。

引用次数: 0

A third-order multiscale analysis and computation for the elliptic problem in arbitrarily heterogeneous domains 任意非均质区域椭圆问题的三阶多尺度分析与计算

IF 2.8 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics Letters

Pub Date : 2026-03-01 Epub Date: 2025-10-30 DOI: 10.1016/j.aml.2025.109806

Qiang Ma , Junzhi Cui

A new third-order multiscale expansion is proposed for the elliptic problem with mixed boundary conditions in arbitrarily heterogeneous domains. The field variable is expanded in terms of a homogenized solution and its derivatives up to the third order. The so-called first to third-order functions are defined to give the homogenized coefficients and correct the differences between the homogenized and original solution both in the domain and on the boundaries. Error estimations are derived, and a typical numerical example is presented demonstrating the high accuracy of the multiscale model. This multiscale analysis presented in this paper generalizes the asymptotic expansion method and can be extended to other problems in non-homogeneous domains.

针对任意非均质域上具有混合边界条件的椭圆型问题，提出了一种新的三阶多尺度展开式。将场变量展开为均质解及其三阶导数的形式。定义了所谓的一阶到三阶函数，以给出均匀化系数，并在定义域和边界上修正均匀化后的解与原解之间的差异。给出了误差估计，并给出了典型的数值算例，证明了多尺度模型具有较高的精度。本文的多尺度分析推广了渐近展开方法，可推广到其他非齐次域的问题。

引用次数: 0

Second-order error analysis for FEM of fractional Laplacian on graded meshes via FDM auxiliary 基于FDM辅助的梯度网格分数阶拉普拉斯有限元二阶误差分析

IF 2.8 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics Letters

Pub Date : 2026-03-01 Epub Date: 2025-10-30 DOI: 10.1016/j.aml.2025.109807

Jianxing Han , Minghua Chen , Yufeng Nie

On graded meshes, the superlinear convergence for fractional Laplacian problem was proved in Borthagaray et al. (2021) by finite element method (FEM). Furthermore, numerical experiments of FEM in Chen, et al. (2021) demonstrate a second-order accuracy on a suitably graded mesh for the 1D case, but a convergence analysis for the proposed scheme remains unavailable. To fill this gap, we provide a second-order error analysis for the resulting FEM algebraic system. Our analysis employs the finite difference method (FDM) as an auxiliary tool based on our previous work [ arXiv:2520.11117], where FEM scheme can be viewed as a modification of the FDM scheme.

Borthagaray et al.（2021）用有限元法证明了分数阶拉普拉斯问题在梯度网格上的超线性收敛性。此外，Chen等人（2021）的有限元数值实验表明，对于一维情况，在适当的分级网格上具有二阶精度，但对所提出方案的收敛性分析仍然不可用。为了填补这一空白，我们对所得到的有限元代数系统进行了二阶误差分析。我们的分析采用有限差分法（FDM）作为辅助工具，基于我们之前的工作[arXiv:2520.11117]，其中FEM方案可以视为FDM方案的修改。

引用次数: 0

The generalized eigenvalue decomposition of a dual quaternion regular matrix pencil 对偶四元数正则矩阵铅笔的广义特征值分解

IF 2.8 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics Letters

Pub Date : 2026-03-01 Epub Date: 2025-11-05 DOI: 10.1016/j.aml.2025.109821

Tao Wang , Ying Li , Mingcui Zhang

With the modeling of dual quaternion matrix in multispectral image, it makes multispectral image compression, denoising, blind source separation and other problems possible. In this paper, we study the generalized eigenvalue decomposition of a dual quaternion regular matrix pencil, and present the corresponding computational method by Hermitian and the skew-Hermitian splitting technique and the generalized eigenvalue decomposition of a quaternion regular matrix pencil. Numerical experiment demonstrates the effectiveness of our computational method.

利用对偶四元数矩阵在多光谱图像中的建模，使多光谱图像压缩、去噪、盲源分离等问题成为可能。本文研究了对偶四元数正则矩阵铅笔的广义特征值分解，给出了相应的计算方法——厄米特分割和斜厄米特分裂技术，以及四元数正则矩阵铅笔的广义特征值分解。数值实验证明了计算方法的有效性。

引用次数: 0

A fourth-order scheme for the exterior Helmholtz problem in polar coordinates 极坐标下外部亥姆霍兹问题的四阶格式

IF 2.8 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics Letters

Pub Date : 2026-03-01 Epub Date: 2025-10-30 DOI: 10.1016/j.aml.2025.109805

Tingting Wu , Jiayuan Liu

In this paper, a fourth-order finite difference scheme is proposed to solve the exterior Helmholtz problem in polar coordinates. The perfectly matched layer (PML) technique is applied to truncate the unbounded domain into a bounded domain, and absorb the outgoing waves. Using the undetermined coefficient method, a fourth-order finite difference scheme for the Helmholtz equation with PML in polar coordinates is established. Numerical results are presented to demonstrate the efficiency and accuracy of the proposed scheme.

本文提出了一种四阶有限差分格式来解决极坐标下的外部亥姆霍兹问题。采用完全匹配层（PML）技术将无界域截断为有界域，吸收出波。利用待定系数法，建立了极坐标系下带PML的亥姆霍兹方程的四阶有限差分格式。数值结果验证了该方法的有效性和准确性。

引用次数: 0

Scattering below the ground state of odd solutions for the focusing INLS in one dimension 一维聚焦INLS奇解在基态下的散射

IF 2.8 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics Letters

Pub Date : 2026-03-01 Epub Date: 2025-11-01 DOI: 10.1016/j.aml.2025.109820

Zhi-Yuan Cui, Yuan Li, Dun Zhao

We consider the one-dimensional focusing inhomogeneous nonlinear Schrödinger equation

i \partial_{t} u + Δ u = - {| x |}^{- b} {| u |}^{α} u,

where

0 < b < 1

and

4 - 2 b < α < \infty

. Although this problem has been extensively studied for initial data in

H^{1} (R^{N})

when

N \geq 2

, there were previously no scattering results available for the case

N = 1

due to the singularity introduced by the term

{| x |}^{- b}

. In this paper, by proving a Virial–Morawetz-type estimate for initial data below a certain level, we establish scattering below the ground state with odd initial data in

H^{1} (R)

我们考虑一维聚焦非齐次非线性Schrödinger方程i∂tu+Δu=−|x|−b|u|αu，其中0<；b<；1和4−2b<；α<∞。虽然对于N≥2时H1（RN）的初始数据已经进行了广泛的研究，但由于术语|x|−b引入的奇异性，之前没有得到N=1情况下的散射结果。本文通过对低于一定水平的初始数据证明一个virial - morawetz型估计，建立了H1(R)中初始数据为奇数的基态下散射。

引用次数: 0

An incremental randomized algorithm for singular value decomposition of streaming data matrices 流数据矩阵奇异值分解的增量随机化算法

IF 2.8 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics Letters

Pub Date : 2026-03-01 Epub Date: 2025-11-06 DOI: 10.1016/j.aml.2025.109822

Yonghe Liu, Fengsheng Wu, Bingxuan Yu, Chaoqian Li

Based on the incremental nature of streaming data and the fast computation of randomized projection algorithms, we propose an incremental randomized algorithm for singular value decomposition (IRSVD) to process streaming data matrices quickly and effectively. The computational complexity of IRSVD is discussed, and the error analysis of IRSVD is provided. Numerical experiments on synthetic data and the recommender system demonstrate the superiority of IRSVD in terms of computational cost.

基于流数据的增量特性和随机化投影算法的快速计算，提出了一种增量随机化奇异值分解（IRSVD）算法来快速有效地处理流数据矩阵。讨论了IRSVD的计算复杂度，并对IRSVD的误差进行了分析。在合成数据和推荐系统上的数值实验证明了IRSVD在计算成本方面的优势。

引用次数: 0

Painlevé integrability, Bäcklund transformation and multi-wave interaction solutions for a generalized (3+1)-dimensional Jimbo–Miwa equation 广义（3+1）维Jimbo-Miwa方程的painlelevel可积性、Bäcklund变换和多波相互作用解

IF 2.8 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics Letters

Pub Date : 2026-03-01 Epub Date: 2025-11-12 DOI: 10.1016/j.aml.2025.109824

Gui-qiong Xu

This paper investigates the integrability and multi-wave interaction solutions for a generalized (3+1)-dimensional Jimbo–Miwa equation, which describes nonlinear waves in fluid dynamics and plasma physics. By applying the Painlevé analysis and the binary Bell polynomial method, we not only derive the integrability conditions, but also obtain the bilinear form, N-soliton solutions, Bäcklund transformation, and Lax pair. Taking the four-soliton solutions as an example, different choices of parameters yield various multi-wave interactions among kink waves, lumps and breathers, revealing rich interaction phenomena in higher-dimensional nonlinear integrable models.

本文研究了流体力学和等离子体物理中描述非线性波的广义（3+1）维Jimbo-Miwa方程的可积性和多波相互作用解。利用painlevel分析和二元Bell多项式方法，我们不仅得到了可积性的条件，而且得到了双线性形式、n -孤子解、Bäcklund变换和Lax对。以四孤子解为例，不同的参数选择会产生不同的多波相互作用，从而揭示了高维非线性可积模型中丰富的相互作用现象。

引用次数: 0

High-order Gauss–Legendre methods admit a composition representation and a conjugate-symplectic counterpart 高阶高斯-勒让德方法允许一个复合表示和一个共轭辛对应

IF 2.8 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics Letters

Pub Date : 2026-03-01 Epub Date: 2025-11-08 DOI: 10.1016/j.aml.2025.109823

Felice Iavernaro , Francesca Mazzia , Ernst Hairer

One of the most classical pairs of symplectic and conjugate-symplectic schemes is given by the Midpoint method (the Gauss–Legendre Runge–Kutta method of order 2) and the Trapezoidal rule. These can be interpreted as compositions of the Implicit and Explicit Euler methods, taken in direct and reverse order, respectively. This naturally raises the question of whether a similar composition structure exists for higher-order Gauss–Legendre methods. In this paper, we provide a positive answer by first examining the fourth-order case and then outlining a generalization to higher orders.

由中点法（2阶高斯-勒让德龙格-库塔法）和梯形法则给出了最经典的辛格式和共轭辛格式。这些可以解释为隐式和显式欧拉方法的组合，分别以正序和反序采取。这自然提出了一个问题：高阶高斯-勒让德方法是否存在类似的组合结构？在本文中，我们通过首先检查四阶情况，然后概述到更高阶的推广，提供了一个肯定的答案。

引用次数: 0

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