数学最新文献

英文中文

IF： -

Stationary Navier–Stokes equations on the half spaces in the scaling critical framework

IF 2.4 2区数学 Q1 MATHEMATICS

Journal of Differential Equations

Pub Date : 2025-04-10 DOI: 10.1016/j.jde.2025.113298

Mikihiro Fujii

In this paper, we consider the inhomogeneous Dirichlet boundary value problem for the stationary Navier–Stokes equations in n-dimensional half spaces

R_{+}^{n} = {x = (x^{'}, x_{n}); x^{'} \in R^{n - 1}, x_{n} > 0}

with

n ⩾ 3

and prove the well-posedness¹ in the scaling critical Besov spaces. Our approach is to regard the system as an evolution equation for the normal variable

x_{n}

and reformulate it as an integral equation. Then, we achieve the goal by making use of the maximal regularity method that has developed in the context of nonstationary analysis in critical Besov spaces. Furthermore, for the case of

n ⩾ 4

, we find that the asymptotic profile of the solution as

x_{n} \to \infty

is given by the

(n - 1)

-dimensional stationary Navier–Stokes flow.

引用次数: 0

Partial boundary regularity for the Navier–Stokes equations in time-dependent domains

IF 2.4 2区数学 Q1 MATHEMATICS

Journal of Differential Equations

Pub Date : 2025-04-10 DOI: 10.1016/j.jde.2025.113299

Dominic Breit

We consider the incompressible Navier–Stokes equations in a moving domain whose boundary is prescribed by a function

η = η (t, y)

(with

y \in R^{2}

) of low regularity. This is motivated by problems from fluid-structure interaction and our result applies, in particular, for linearised Koiter shells with dissipation. We prove partial boundary regularity for boundary suitable weak solutions assuming that η is continuous in time with values in the fractional Sobolev space

W_{y}^{2 - 1 / p, p}

for some

p > 15 / 4

and we have

\partial_{t} η \in L_{t}^{3} (W_{y}^{1, q_{0}})

for some

q_{0} > 2

The existence of boundary suitable weak solutions is a consequence of a new maximal regularity result for the Stokes equations in moving domains which is of independent interest.

引用次数: 0

Uniqueness of cylindrically symmetric solutions for coupled Gross-Pitaevskii equations with totally degenerate potentials

IF 2.4 2区数学 Q1 MATHEMATICS

Journal of Differential Equations

Pub Date : 2025-04-10 DOI: 10.1016/j.jde.2025.113288

Xiaoyu Zeng, Huan-Song Zhou

For a couple of singularly perturbed Gross-Pitaevskii equations, we prove that the single peak solutions concentrating at the same point are unique provided that the Taylor's expansion of potentials

V_{1} (x), V_{2} (x)

around the concentration point has the same order along all directions. Under suitable conditions, our results imply that the peak solutions obtained in [21], [31], [38] are unique. Moreover, if the radially symmetric ring-shaped potential attains its minimum at some spheres

Γ_{j} : = {x \in R^{N} : | x | = A_{j} > 0}, j = 1, 2, \dots, l

, and is totally degenerate in the tangential space of

Γ_{i}

, we prove that the positive ground state is cylindrically symmetric and unique up to rotations around the origin. As far as we know, this seems to be the first uniqueness result for ground states under radially symmetric but non-monotonic potentials.

{"title":"Uniqueness of cylindrically symmetric solutions for coupled Gross-Pitaevskii equations with totally degenerate potentials","authors":"Xiaoyu Zeng, Huan-Song Zhou","doi":"10.1016/j.jde.2025.113288","DOIUrl":"10.1016/j.jde.2025.113288","url":null,"abstract":"<div><div>For a couple of singularly perturbed Gross-Pitaevskii equations, we prove that the single peak solutions concentrating at the same point are unique provided that the Taylor's expansion of potentials <math><msub><mrow><mi>V</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>(</mo><mi>x</mi><mo>)</mo><mo>,</mo><msub><mrow><mi>V</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>(</mo><mi>x</mi><mo>)</mo></math> around the concentration point has the same order along all directions. Under suitable conditions, our results imply that the peak solutions obtained in [21], [31], [38] are unique. Moreover, if the radially symmetric ring-shaped potential attains its minimum at some spheres <math><msub><mrow><mi>Γ</mi></mrow><mrow><mi>j</mi></mrow></msub><mo>:</mo><mo>=</mo><mo>{</mo><mi>x</mi><mo>∈</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>N</mi></mrow></msup><mo>:</mo><mo>|</mo><mi>x</mi><mo>|</mo><mo>=</mo><msub><mrow><mi>A</mi></mrow><mrow><mi>j</mi></mrow></msub><mo>></mo><mn>0</mn><mo>}</mo><mo>,</mo><mi>j</mi><mo>=</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mo>⋯</mo><mo>,</mo><mi>l</mi></math>, and is totally degenerate in the tangential space of <math><msub><mrow><mi>Γ</mi></mrow><mrow><mi>i</mi></mrow></msub></math>, we prove that the positive ground state is cylindrically symmetric and unique up to rotations around the origin. As far as we know, this seems to be the first uniqueness result for ground states under radially symmetric but non-monotonic potentials.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"434 ","pages":"Article 113288"},"PeriodicalIF":2.4,"publicationDate":"2025-04-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143807901","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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

The saturation number for unions of four cliques

IF 0.7 3区数学 Q2 MATHEMATICS

Discrete Mathematics

Pub Date : 2025-04-10 DOI: 10.1016/j.disc.2025.114532

Ruo-Xuan Li, Rong-Xia Hao, Zhen He, Wen-Han Zhu

A graph G is H-saturated if G does not contain a copy of H, but the addition of any edge

e \in \overline{G}

would create a copy of H. The saturation number

s a t (n, H)

for a graph H is the minimal number of edges in any H-saturated graph of order n. The

s a t (n, K_{p_{1}} \cup K_{p_{2}} \cup K_{p_{3}})

with

p_{3} \geq p_{1} + p_{2}

was determined in [Discrete Math. 347 (2024) 113868]. In this paper,

s a t (n, K_{p_{1}} \cup K_{p_{2}} \cup K_{p_{3}} \cup K_{p_{4}})

with

p_{i + 1} - p_{i} \geq p_{1}

for

2 \leq i \leq 3

and

4 \leq p_{1} \leq p_{2}

is determined.

引用次数: 0

Stephen D. Cohen's contributions to the finite fields community

IF 1.2 3区数学 Q1 MATHEMATICS

Finite Fields and Their Applications

Pub Date : 2025-04-10 DOI: 10.1016/j.ffa.2025.102627

Sophie Huczynska, Gary L. Mullen

In this short note, to mark the retirement of Stephen D. Cohen from his editorial role at this journal, we discuss and acknowledge his significant contributions to the finite fields community in the areas of service and research.

引用次数: 0

On Aharonov-Bohm operators with multiple colliding poles of any circulation

IF 1.3 2区数学 Q1 MATHEMATICS

Nonlinear Analysis-Theory Methods & Applications

Pub Date : 2025-04-10 DOI: 10.1016/j.na.2025.113813

Veronica Felli , Benedetta Noris , Giovanni Siclari

This paper deals with quantitative spectral stability for Aharonov-Bohm operators with many colliding poles of whichever circulation. An equivalent formulation of the eigenvalue problem is derived as a system of two equations with real coefficients, coupled through prescribed jumps of the unknowns and their normal derivatives across the segments joining the poles with the collision point. Under the assumption that the sum of all circulations is not integer, the dominant term in the asymptotic expansion for eigenvalues is characterized in terms of the minimum of an energy functional associated with the configuration of poles. Estimates of the order of vanishing of the eigenvalue variation are then deduced from a blow-up analysis, yielding sharp asymptotics in some particular examples.

引用次数: 0

An agent-based model for simulating cooperative behavior in crowd evacuation during toxic gas terrorist attacks

IF 5.3 1区数学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Chaos Solitons & Fractals

Pub Date : 2025-04-10 DOI: 10.1016/j.chaos.2025.116397

Peng Lu , Yufei Li

Toxic gas leaks pose severe threats to public safety and societal stability, leading to large-scale casualties and social panic. This paper focuses on crowd evacuation behavior during toxic gas leak incidents, proposing an evacuation model that combines Computational Fluid Dynamics (CFD) and Agent-Based Modeling (ABM). By introducing a helping mechanism among agents with prosocial personalities, the study examines the impact of the prosocial personality ratio (p) on evacuation time, fatalities, and severe injuries. Subsequently, the effects of the p under varying conditions, such as total population size and evacuation response time, are explored. Additionally, a Random Forest model is employed to accurately predict evacuation risks, and the NSGA-III multi-objective optimization algorithm is utilized to identify the optimal range of p across different scenarios. The results indicate that a reasonable proportion of prosocial personalities can significantly reduce fatality rates and enhance overall evacuation efficiency. However, an excessively high proportion of prosocial individuals may increase crowd casualties due to extended delays caused by helping behaviors. This study contributes to the body of knowledge on public safety, provides methodological references for developing evacuation strategies during toxic gas diffusion incidents, and offers guidance for future emergency management practices.

{"title":"An agent-based model for simulating cooperative behavior in crowd evacuation during toxic gas terrorist attacks","authors":"Peng Lu , Yufei Li","doi":"10.1016/j.chaos.2025.116397","DOIUrl":"10.1016/j.chaos.2025.116397","url":null,"abstract":"<div><div>Toxic gas leaks pose severe threats to public safety and societal stability, leading to large-scale casualties and social panic. This paper focuses on crowd evacuation behavior during toxic gas leak incidents, proposing an evacuation model that combines Computational Fluid Dynamics (CFD) and Agent-Based Modeling (ABM). By introducing a helping mechanism among agents with prosocial personalities, the study examines the impact of the prosocial personality ratio (p) on evacuation time, fatalities, and severe injuries. Subsequently, the effects of the p under varying conditions, such as total population size and evacuation response time, are explored. Additionally, a Random Forest model is employed to accurately predict evacuation risks, and the NSGA-III multi-objective optimization algorithm is utilized to identify the optimal range of p across different scenarios. The results indicate that a reasonable proportion of prosocial personalities can significantly reduce fatality rates and enhance overall evacuation efficiency. However, an excessively high proportion of prosocial individuals may increase crowd casualties due to extended delays caused by helping behaviors. This study contributes to the body of knowledge on public safety, provides methodological references for developing evacuation strategies during toxic gas diffusion incidents, and offers guidance for future emergency management practices.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"196 ","pages":""},"PeriodicalIF":5.3,"publicationDate":"2025-04-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143807113","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

A note on extremal trees for a bound on the double domination number

IF 1 3区数学 Q3 MATHEMATICS, APPLIED

Discrete Applied Mathematics

Pub Date : 2025-04-10 DOI: 10.1016/j.dam.2025.04.007

Ravi Kalaiyarasi , Mustapha Chellali , Yanamandram B. Venkatakrishnan

In a graph

G,

a vertex is said to dominate itself and its neighbors. A subset

D

V (G)

is a double dominating set if every vertex of

V (G)

is dominated at least twice by the vertices of

D

. The double domination number

γ_{\times 2} (G)

is the minimum cardinality among all double dominating sets of

G

. Cabrera-Martínez proved that for every nontrivial tree

T

of order

n (T)

with

ℓ (T)

leaves and

s (T)

support vertices,

γ_{\times 2} (T) \geq \frac{1}{2} (n (T) - γ (T) + ℓ (T) + s (T) + 1),

where

γ (T)

stands for the domination number of

T .

In this note, we provide a constructive characterization of trees attaining this bound in response to the problem raised by Cabrera-Martínez.

引用次数: 0

Stratification of three-dimensional real flows II: A generalization of Poincaré's planar sectorial decomposition

IF 2.4 2区数学 Q1 MATHEMATICS

Journal of Differential Equations

Pub Date : 2025-04-10 DOI: 10.1016/j.jde.2025.113292

Clementa Alonso-González , Fernando Sanz Sánchez

Let ξ be an analytic vector field in

R^{3}

with an isolated singularity at the origin and having only hyperbolic singular points after a reduction of singularities

π : M \to R^{3}

. Assuming certain conditions to be specified throughout the work at hand, we establish a theorem of stratification of the dynamics of ξ that generalizes to dimension three the classical one, coming from Poincaré, about the decomposition of the dynamics of an analytic planar vector field into parabolic, elliptic or hyperbolic invariant sectors.

引用次数: 0

Decomposition family and spectral extremal problems on non-bipartite graphs

IF 0.7 3区数学 Q2 MATHEMATICS

Discrete Mathematics

Pub Date : 2025-04-10 DOI: 10.1016/j.disc.2025.114527

Longfei Fang , Michael Tait , Mingqing Zhai

<div><div>Given a graph family <math><mi>H</mi></math> with <math><msub><mrow><mi>min</mi></mrow><mrow><mi>H</mi><mo>∈</mo><mi>H</mi></mrow></msub><mo>⁡</mo><mi>χ</mi><mo>(</mo><mi>H</mi><mo>)</mo><mo>=</mo><mi>r</mi><mo>+</mo><mn>1</mn><mo>≥</mo><mn>3</mn></math>. Let <math><mrow><mi>ex</mi></mrow><mo>(</mo><mi>n</mi><mo>,</mo><mi>H</mi><mo>)</mo></math> and <math><mrow><mi>spex</mi></mrow><mo>(</mo><mi>n</mi><mo>,</mo><mi>H</mi><mo>)</mo></math> be the maximum number of edges and the maximum spectral radius of the adjacency matrix over all n-vertex <math><mi>H</mi></math>-free graphs, respectively. Denote by <math><mrow><mi>EX</mi></mrow><mo>(</mo><mi>n</mi><mo>,</mo><mi>H</mi><mo>)</mo></math> (resp. <math><mrow><mi>SPEX</mi></mrow><mo>(</mo><mi>n</mi><mo>,</mo><mi>H</mi><mo>)</mo></math>) the set of extremal graphs with respect to <math><mrow><mi>ex</mi></mrow><mo>(</mo><mi>n</mi><mo>,</mo><mi>H</mi><mo>)</mo></math> (resp. <math><mrow><mi>spex</mi></mrow><mo>(</mo><mi>n</mi><mo>,</mo><mi>H</mi><mo>)</mo></math>). A fundamental problem in extremal spectral graph theory asks which graph H satisfies <math><mrow><mi>SPEX</mi></mrow><mo>(</mo><mi>n</mi><mo>,</mo><mi>H</mi><mo>)</mo><mo>⊆</mo><mrow><mi>EX</mi></mrow><mo>(</mo><mi>n</mi><mo>,</mo><mi>H</mi><mo>)</mo></math>.</div><div>Wang et al. (2023) [43] proved that <math><mrow><mi>SPEX</mi></mrow><mo>(</mo><mi>n</mi><mo>,</mo><mi>H</mi><mo>)</mo><mo>⊆</mo><mrow><mi>EX</mi></mrow><mo>(</mo><mi>n</mi><mo>,</mo><mi>H</mi><mo>)</mo></math> for n sufficiently large and any finite graph H with <math><mrow><mi>ex</mi></mrow><mo>(</mo><mi>n</mi><mo>,</mo><mi>H</mi><mo>)</mo><mo>=</mo><mi>e</mi><mo>(</mo><msub><mrow><mi>T</mi></mrow><mrow><mi>n</mi><mo>,</mo><mi>r</mi></mrow></msub><mo>)</mo><mo>+</mo><mi>O</mi><mo>(</mo><mn>1</mn><mo>)</mo></math>. In this paper, we use decomposition family defined by Simonovits to give a characterization of which graph families <math><mi>H</mi></math> satisfy <math><mi>e</mi><mo>(</mo><msub><mrow><mi>T</mi></mrow><mrow><mi>n</mi><mo>,</mo><mi>r</mi></mrow></msub><mo>)</mo><mo>≤</mo><mrow><mi>ex</mi></mrow><mo>(</mo><mi>n</mi><mo>,</mo><mi>H</mi><mo>)</mo><mo><</mo><mi>e</mi><mo>(</mo><msub><mrow><mi>T</mi></mrow><mrow><mi>n</mi><mo>,</mo><mi>r</mi></mrow></msub><mo>)</mo><mo>+</mo><mo>⌊</mo><mfrac><mrow><mi>n</mi></mrow><mrow><mn>2</mn><mi>r</mi></mrow></mfrac><mo>⌋</mo></math>. Using this result, we show that <math><mrow><mi>SPEX</mi></mrow><mo>(</mo><mi>n</mi><mo>,</mo><mi>H</mi><mo>)</mo><mo>⊆</mo><mrow><mi>EX</mi></mrow><mo>(</mo><mi>n</mi><mo>,</mo><mi>H</mi><mo>)</mo></math> for n sufficiently large and any finite family <math><mi>H</mi></math> with <math><mi>e</mi><mo>(</mo><ms

引用次数: 0

下一页尾页

类型

数学最新文献

全部化学•材料生命科学医学物理工程技术环境•农林材料科学地球科学法学管理学化学环境科学与生态学计算机科学教育学经济学农林科学人文科学生物学数学物理与天体物理心理学综合性期刊其他工业工程理学历史学农学文学信息工程

数据库

全部 ACS Publications Elsevier ieeexplore Springer The Royal Society of Chemistry Wiley

期刊

全部 Dokl. Math. Funct. Anal. Appl. J. Homotopy Relat. Struct. J. Math. Fluid Mech. Math. Phys. Anal. Geom. ACTA MATH APPL SIN-E Adv. Nonlinear Stud. Adv. Appl. Clifford Algebras ADV GEOM ALGEBR LOG+ Am. J. Math. Am. Math. Mon. ANN I H POINCARE-PR APPL CATEGOR STRUCT ANN STAT ANN MATH Appl. Numer. Math. Ann. Mat. Pura Appl. Ann. Global Anal. Geom. Arch. Math. Archiv. Math. Logic BIOMETRICS BIOMETRIKA Bull. Math. Sci Bull. Math. Biol. B IRAN MATH SOC Calc. Var. Partial Differ. Equations Bull. Am. Math. Soc. CALCOLO CHAOS SOLITON FRACT CHAOS COMB PROBAB COMPUT COMMUN STAT-THEOR M Commun. Math. Stat. Commun. Pure Appl. Math. C.R. Math. Commun. Pure Appl. Anal. Demonstratio Mathematica Des. Codes Cryptogr. Duke Math. J. Electron. J. Comb. FILOMAT FORUM MATH Fractal and Fractional Geom. Funct. Anal. GRAPH COMBINATOR INTEGR EQUAT OPER TH INT J ALGEBR COMPUT Interfaces Free Boundaries Int. J. Comput. Math. INT J NUMBER THEORY INVENT MATH Int. Math. Res. Not. Int. Stat. Rev. Isr. J. Math. J. Algebra J ALGEBR COMB J. Appl. Math. Comput. J. Appl. Stat. J. Comb. Des. J. Comput. Graphical Stat. J. Complex Networks J. Differ. Equations Appl. J. Differ. Equations J. Dyn. Differ. Equations J. Differ. Geom. J. Funct. Anal. J. Funct. Spaces J. Global Optim. J.Fourier Anal. Appl. J. Graph Theory J. Inequal. Appl. J. Math. Imaging Vision J. Multivar. Anal. J. Symb. Log. Journal of Survey Statistics and Methodology J. Am. Stat. Assoc. Linear Algebra Appl. Math. Z. MATH SLOVACA Math. Modell. Nat. Phenom. Math. Notes Math. Program. MATHEMATICS-BASEL Math. Ann. Math. Proc. Cambridge Philos. Soc. METHODOL COMPUT APPL Math. Comput. MATHEMATIKA Numer. Methods Partial Differ. Equations PHYSICA D Probab. Theory Relat. Fields Proc. Edinburgh Math. Soc. Proc. Am. Math. Soc. Q. Appl. Math. Ric. Mat. Stochastic Models STAT COMPUT TAIWAN J MATH TOPOL METHOD NONL AN

﹀