Journal of Differential Equations最新文献

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Dynamical versions of Morgan's uncertainty principle and electromagnetic Schrödinger evolutions 摩根测不准原理的动力学版本和电磁Schrödinger演化

IF 2.3 2区数学 Q1 MATHEMATICS

Journal of Differential Equations

Pub Date : 2026-01-30 DOI: 10.1016/j.jde.2026.114159

Shanlin Huang , Zhenqiang Wang

This paper investigates the unique continuation properties of solutions of the electromagnetic Schrödinger equation

i \partial_{t} u (x, t) + {(\nabla - i A)}^{2} u (x, t) = V (x, t) u (x, t) in R^{d} \times [0, 1],

where A represents a time-independent magnetic vector potential and V is a bounded, complex valued time-dependent potential. Given

1 < p < 2

and

1 / p + 1 / q = 1

, we prove that there exists

N_{p} > 0

such that if

\int_{R^{d}} | u (x, 0) |^{2} e^{2 α^{p} | x |^{p} / p} d x + \int_{R^{d}} | u (x, 1) |^{2} e^{2 β^{q} | x |^{q} / q} d x < \infty

for some

α, β > 0

, and if

α β > N_{p}

, then

u \equiv 0

. These results can be interpreted as dynamical versions of the uncertainty principle of Morgan's type. Furthermore, as an application, our results extend to a large class of semi-linear Schrödinger equations.

本文研究了电磁Schrödinger方程i∂tu(x,t)+(∇−iA)2u(x,t)=V(x,t)u(x,t) inrdx[0,1]解的唯一连续性质，其中A表示时无关的磁矢量势，V是有界的复值时相关势。给定1<；p<；2和1/p+1/q=1，我们证明了Np>；0的存在，使得∫Rd|u(x,0) |e2α - p|x|p/pdx+∫Rd|u(x,1)|2e2βq|x|q/qdx<；∞对于某些α，β>0，且αβ>；Np，则u≡0。这些结果可以解释为摩根不确定性原理的动态版本。此外，作为一个应用，我们的结果推广到一类半线性Schrödinger方程。

引用次数: 0

Large time behavior of solutions to unipolar Euler-Poisson equations with space-dependent damping 具有空间相关阻尼的单极欧拉-泊松方程解的大时间行为

IF 2.3 2区数学 Q1 MATHEMATICS

Journal of Differential Equations

Pub Date : 2026-01-30 DOI: 10.1016/j.jde.2026.114172

Chunpeng Wang, Jianing Xu

This paper is concerned with the Cauchy problem to Euler-Poisson equations for one-dimensional unipolar hydrodynamic model of semiconductors with damping of space-dependent coefficient. Under some smallness assumptions on the initial data, we establish the global existence of smooth solutions to the Cauchy problem by applying the energy methods. It is shown that the solutions to unipolar Euler-Poisson equations with space-dependent damping time-exponentially converge to the stationary solutions. No smallness assumption is imposed on the space-dependent coefficient of damping.

本文研究了具有空间依赖系数阻尼的一维单极半导体流体力学模型的欧拉-泊松方程的Cauchy问题。在初始数据的一些较小的假设条件下，利用能量方法建立了柯西问题光滑解的全局存在性。证明了具有空间相关阻尼的单极欧拉-泊松方程的解在时间指数上收敛于平稳解。对阻尼的空间相关系数不作小的假设。

引用次数: 0

Quantitative blow-up via renormalized Kato theory: Resolving Nakao-type systems 通过重整加藤理论的定量爆炸：解决中尾型系统

IF 2.3 2区数学 Q1 MATHEMATICS

Journal of Differential Equations

Pub Date : 2026-01-29 DOI: 10.1016/j.jde.2026.114165

Mengyun Liu

We address the fundamental obstruction identified in [10, Remark 3] for system (1) where sign-changing kernels when

b^{2} < 4 k

preclude blow-up arguments via nonnegative functionals—by partially resolving it in the regime

b^{2} < k

Building upon Kato-type techniques, we develop a renormalized iteration scheme establishing the quantitative upper bounds for blow-up times. This framework resolves the critical case

b^{2} < k

for

b, k > 0

under

θ (p, q, n) : = \frac{1}{p q - 1} - \frac{n - 1}{2} \geq 0

. When combined with [10]'s results for

b^{2} \geq 4 k

, it completes the blow-up theory for the subregime

b^{2} < k

. For

b, k < 0

, we prove blow-up in the extended critical region

Γ_{_{G G}} (p, q, n) : = \max {\frac{p + 1}{p q - 1}, \frac{q + 1}{p q - 1}} - \frac{n - 1}{2} \geq 0,

strictly containing the classical critical set.

我们解决了在系统(1)中[10，Remark 3]中发现的基本障碍，其中当b2<；4k时的符号变化核通过非负泛函排除了爆炸参数-通过在b2<；k中部分解决了它。在加藤型技术的基础上，我们开发了一种重归一化的迭代方案，建立了爆炸时间的定量上界。该框架解决了在θ(p,q,n) =1pq−1−n−12≥0的情况下，b,k, b2<；k的临界情况。结合[10]在b2≥4k时的结果，完成了子区b2<；k的爆破理论。对于b，k<0，证明了扩展临界regionΓGG（p,q,n）的爆破性：=max (p +1pq−1,q+1pq−1}−n−12≥0，严格包含经典临界集。

引用次数: 0

Asymptotic stability of viscous shock profiles to Burgers equation with singular super-fast diffusion 具有奇异超快扩散的Burgers方程的粘性激波曲线的渐近稳定性

IF 2.3 2区数学 Q1 MATHEMATICS

Journal of Differential Equations

Pub Date : 2026-01-28 DOI: 10.1016/j.jde.2026.114158

Jingyu Li , Xiaowen Li , Ming Mei

This paper is concerned with the large time behaviors of solutions to the Burgers equation of porous-media type in the form of

u_{t} + f {(u)}_{x} = {(u^{m - 1} u_{x})}_{x}

, where the diffusion

{(u^{m - 1} u_{x})}_{x} = {(\frac{u_{x}}{u^{1 + | m |}})}_{x}

with

m < 0

possesses the strong singularity of fast-diffusion at

u = 0

. The main issue of the paper is to show the asymptotic stability of viscous shock profiles with the constant states

u_{-} > u_{+} = 0

, where the strong singularity exhibits for the equation when the viscous shock wave reaches the singular point

u_{+} = 0

. To overcome such a strong singularity for wave stability, we first need to analyze the rate of the viscous shock wave to

u_{+} = 0

, then we artfully choose some weight functions which are closely dependent on the decay rate of the viscous shock wave to the singular point

u_{+} = 0

, and further show the wave stability by the weighted-energy-method.

本文研究了多孔介质型Burgers方程ut+f(u)x=(um - 1ux)x形式解的大时间性质，其中扩散（um - 1ux）x=(uxu1+|m|)x与m<；0在u=0处具有快速扩散的强奇异性。本文的主要问题是证明恒定状态u−>；u+=0时粘性激波剖面的渐近稳定性，其中当粘性激波到达奇点u+=0时，方程表现出强奇异性。为了克服这种强奇异性，我们首先需要分析粘性激波到u+=0的速率，然后巧妙地选择一些与粘性激波到奇异点u+=0的衰减速率密切相关的权函数，并进一步用加权能量法来表示波的稳定性。

引用次数: 0

Matrix-weighted Besov–Triebel–Lizorkin spaces of optimal scale: Real-variable characterizations, invariance on integrable index, and Sobolev-type embedding 最优尺度的矩阵加权besov - triiebel - lizorkin空间：实变量表征、可积指标的不变性和sobolev型嵌入

IF 2.3 2区数学 Q1 MATHEMATICS

Journal of Differential Equations

Pub Date : 2026-01-28 DOI: 10.1016/j.jde.2026.114140

Fan Bu, Dachun Yang, Wen Yuan, Mingdong Zhang

Using growth functions, we introduce generalized matrix-weighted Besov–Triebel–Lizorkin-type spaces with matrix

A_{\infty}

weights. We first characterize these spaces, respectively, in terms of the φ-transform, the Peetre-type maximal function, and the Littlewood–Paley functions. Furthermore, after establishing the boundedness of almost diagonal operators on the corresponding sequence spaces, we obtain the molecular and the wavelet characterizations of these spaces. As applications, we find the sufficient and necessary conditions for the invariance of those Triebel–Lizorkin-type spaces on the integrable index and also for the Sobolev-type embedding of all these spaces. The main novelty exists in that these results are of wide generality, the growth condition of growth functions is not only sufficient but also necessary for the boundedness of almost diagonal operators and hence this new framework of Besov–Triebel–Lizorkin-type is optimal, some results either are new or improve the known ones even for known matrix-weighted Besov–Triebel–Lizorkin spaces, and, furthermore, even in the scalar-valued setting, all the results are also new.

利用生长函数，引入了权矩阵为A∞的广义矩阵加权besov - triiebel - lizorkin型空间。我们首先分别用φ-变换、peete型极大函数和Littlewood-Paley函数来描述这些空间。在建立了相应序列空间上的概对角算子的有界性后，得到了这些空间的分子特征和小波特征。作为应用，我们得到了这些triiebel - lizorkin型空间在可积指标上的不变性和所有这些空间的sobolev型嵌入的充分必要条件。主要的新颖之处是这些结果具有广泛的通用性，生长函数的生长条件对于几乎对角算子的有界性不仅是充分的，而且是必要的，因此这个新的besov - triiebel - lizorkin型框架是最优的，甚至对于已知的矩阵加权besov - triiebel - lizorkin空间，有些结果是新的或改进了已知的结果，甚至在标量值设置下，所有的结果也是新的。

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引用次数: 0

Stability and exponential decay for the 2D anisotropic Boussinesq equations near the hydrostatic equilibrium 流体静力平衡附近二维各向异性Boussinesq方程的稳定性和指数衰减

IF 2.3 2区数学 Q1 MATHEMATICS

Journal of Differential Equations

Pub Date : 2026-01-28 DOI: 10.1016/j.jde.2026.114160

Kaibin Zhang , Xinhua Li , Chunyou Sun

In this paper, we focus on the stability and long-time behavior problem for the 2D Boussinesq equations near the hydrostatic equilibrium with partial dissipation in the velocity and horizontal thermal diffusion. The lack of dissipation in the first component of the velocity and vertical thermal diffusion leads to the main difficulties. We establish the stability in

H^{2}

, and demonstrate the exponential decay of its oscillatory portion in the

H^{1}

本文研究了具有速度和水平热扩散部分耗散的二维Boussinesq方程在流体静力平衡附近的稳定性和长期行为问题。在速度的第一分量和垂直热扩散中缺乏耗散是主要的困难。我们建立了它在H2中的稳定性，并证明了它的振荡部分在H1中的指数衰减。

引用次数: 0

An improved version of a spectral inequality by Payne 佩恩谱不等式的改进版本

IF 2.3 2区数学 Q1 MATHEMATICS

Journal of Differential Equations

Pub Date : 2026-01-28 DOI: 10.1016/j.jde.2026.114138

Paolo Acampora , Emanuele Cristoforoni , Carlo Nitsch , Cristina Trombetti

A celebrated inequality by Payne relates the first eigenvalue of the Dirichlet Laplacian to the first eigenvalue of the buckling problem. Motivated by the goal of establishing a quantitative version of this inequality, we show that Payne's original estimate—which is not sharp—can in fact be improved. Our result provides a refined spectral bound and opens the way to further investigations into quantitative enhancements of classical inequalities in spectral theory.

佩恩的一个著名不等式将狄利克雷拉普拉斯函数的第一特征值与屈曲问题的第一特征值联系起来。在建立这个不等式的定量版本的目标的激励下，我们表明Payne的原始估计——它并不清晰——实际上可以改进。我们的结果提供了一个精细的谱界，并为进一步研究谱理论中经典不等式的定量增强开辟了道路。

引用次数: 0

Stability of 2D tropical climate system with partial dissipations near Couette flow Couette流附近部分耗散的二维热带气候系统的稳定性

IF 2.3 2区数学 Q1 MATHEMATICS

Journal of Differential Equations

Pub Date : 2026-01-28 DOI: 10.1016/j.jde.2026.114148

Dongjuan Niu , Huiru Wu , Jiahong Wu , Xiaojing Xu

The Tropical Climate Model (TCM) is a simplified system that captures key aspects of equatorial atmospheric dynamics through the interaction of barotropic and baroclinic velocity modes with temperature fields. This study focuses on the nonlinear stability of Couette flow in a two-dimensional TCM with only partial dissipation. Two main difficulties arise: the absence of full dissipation, and the lack of a divergence-free condition for the baroclinic velocity. To address these challenges, we develop a refined Fourier multiplier approach that captures enhanced dissipation via the interaction between the shear-induced mixing term and vertical viscosity. Furthermore, this paper introduces new techniques to handle terms involving non-divergence-free components and exploits key couplings within the system to control potentially unstable linear terms. Under appropriate smallness conditions on the initial perturbations in anisotropic Sobolev spaces, we rigorously establish the nonlinear stability of the Couette flow and identify a possible precise transition threshold for stability.

热带气候模式（TCM）是一个简化的系统，它通过正压和斜压速度模式与温度场的相互作用来捕捉赤道大气动力学的关键方面。本文研究了仅部分耗散的二维TCM中Couette流的非线性稳定性。出现了两个主要困难：缺乏充分耗散，以及缺乏斜压速度的无散度条件。为了解决这些挑战，我们开发了一种改进的傅立叶乘数方法，通过剪切诱导的混合项和垂直粘度之间的相互作用来捕获增强的耗散。此外，本文还介绍了处理涉及非无散度分量的项的新技术，并利用系统内的关键耦合来控制潜在不稳定的线性项。在各向异性Sobolev空间初始扰动较小的条件下，我们严格地建立了Couette流的非线性稳定性，并确定了可能的精确过渡阈值。

引用次数: 0

Stability and sharp decay for the 3D incompressible anisotropic Navier-Stokes equations with fractional horizontal dissipation 具有分数水平耗散的三维不可压缩各向异性Navier-Stokes方程的稳定性和急剧衰减

IF 2.3 2区数学 Q1 MATHEMATICS

Journal of Differential Equations

Pub Date : 2026-01-28 DOI: 10.1016/j.jde.2026.114167

Qunyi Bie , Hui Fang , Shu Wang , Yanping Zhou

This paper aims to study the global stability and long-time behavior of the three-dimensional incompressible anisotropic Navier-Stokes equations with only fractional horizontal dissipation. The absence of vertical dissipation induces substantial analytical difficulties, rendering classical methods such as Schonbek's Fourier splitting technique inapplicable. By developing refined anisotropic energy estimates that exploit both the divergence-free condition and the structure of the dissipation, we establish the global existence and asymptotic stability of small solutions in Sobolev spaces under weaker dissipation conditions than previously known. Furthermore, for suitably regular initial data, we prove sharp decay rates for the solution and its first-order derivatives. Our results substantially enlarge the admissible parameter regime and provide robust analytical tools that may also be applied to other fractional anisotropic fluid models.

本文旨在研究具有分数阶水平耗散的三维不可压缩各向异性Navier-Stokes方程的全局稳定性和长时性。垂直耗散的缺失导致了大量的分析困难，使得经典方法如Schonbek的傅立叶分裂技术不适用。通过发展利用无散度条件和耗散结构的精细各向异性能量估计，我们建立了Sobolev空间中小解在较弱耗散条件下的整体存在性和渐近稳定性。此外，对于适当规则的初始数据，我们证明了解及其一阶导数的急剧衰减率。我们的结果大大扩大了可接受的参数范围，并提供了健壮的分析工具，也可以应用于其他分数各向异性流体模型。

引用次数: 0

Blow-up solutions for general Toda systems on Riemann surfaces 黎曼曲面上一般Toda系统的爆破解

IF 2.3 2区数学 Q1 MATHEMATICS

Journal of Differential Equations

Pub Date : 2026-01-28 DOI: 10.1016/j.jde.2026.114145

Zhengni Hu, Miaomiao Zhu

In this paper, we study general Toda systems with homogeneous Neumann boundary conditions on Riemann surfaces. Assuming the surface satisfies the “k-symmetric” condition, we construct a family of bubbling solutions using singular perturbation methods, where the concentration rates of different components occur in distinct orders. In particular, we establish the existence of asymmetric blow-up solutions for the

S U (3)

Toda system. Furthermore, the blow-up points are precisely located at the “k-symmetric” centers of the surface.

本文研究了黎曼曲面上具有齐次诺伊曼边界条件的一般Toda系统。假设表面满足“k对称”条件，我们用奇异摄动方法构造了一组冒泡解，其中不同组分的浓度率以不同的顺序出现。特别地，我们建立了SU(3) Toda系统的不对称爆破解的存在性。此外，爆炸点精确地位于表面的“k对称”中心。

引用次数: 0

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