Archive for Rational Mechanics and Analysis最新文献_第7页

Sustained Oscillations in Hyperbolic–Parabolic Systems 双曲抛物线系统中的持续振荡

IF 2.6 1区数学

Archive for Rational Mechanics and Analysis Pub Date : 2024-05-25 DOI: 10.1007/s00205-024-01999-5

Athanasios E. Tzavaras

引用次数: 0

Smooth Transonic Flows with Nonzero Vorticity to a Quasi Two Dimensional Steady Euler Flow Model 准二维稳定欧拉流模型的非零涡度平滑跨声速流动

IF 2.6 1区数学

Archive for Rational Mechanics and Analysis Pub Date : 2024-05-22 DOI: 10.1007/s00205-024-02000-z

Shangkun Weng, Zhouping Xin

{"title":"Smooth Transonic Flows with Nonzero Vorticity to a Quasi Two Dimensional Steady Euler Flow Model","authors":"Shangkun Weng, Zhouping Xin","doi":"10.1007/s00205-024-02000-z","DOIUrl":"10.1007/s00205-024-02000-z","url":null,"abstract":"<div>This paper concerns smooth transonic flows with nonzero vorticity in De Laval nozzles for a quasi two dimensional steady Euler flow model which is a generalization of the classical quasi one dimensional model. First we examine the existence and uniqueness of smooth transonic flows to the quasi one-dimensional model, which start from a subsonic state at the entrance and accelerate to reach a sonic state at the throat and then become supersonic are proved by a reduction of degeneracy of the velocity near the sonic point and the implicit function theorem. These flows can have positive or zero acceleration at their sonic points and the degeneracy types near the sonic point are classified precisely. We then establish the structural stability of the smooth one dimensional transonic flow with positive acceleration at the sonic point for the quasi two dimensional steady Euler flow model under small perturbations of suitable boundary conditions, which yields the existence and uniqueness of a class of smooth transonic flows with nonzero vorticity and positive acceleration to the quasi two dimensional model. The positive acceleration of the one dimensional transonic solutions plays an important role in searching for an appropriate multiplier for the linearized second order mixed type equations. A deformation-curl decomposition for the quasi two dimensional model is utilized to deal with the transonic flows with nonzero vorticity.</div>","PeriodicalId":55484,"journal":{"name":"Archive for Rational Mechanics and Analysis","volume":null,"pages":null},"PeriodicalIF":2.6,"publicationDate":"2024-05-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141146764","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

Convergence Rates and Fluctuations for the Stokes–Brinkman Equations as Homogenization Limit in Perforated Domains 作为穿孔域均质化极限的斯托克斯-布林克曼方程的收敛速率和波动

IF 2.6 1区数学

Archive for Rational Mechanics and Analysis Pub Date : 2024-05-22 DOI: 10.1007/s00205-024-01993-x

Richard M. Höfer, Jonas Jansen

{"title":"Convergence Rates and Fluctuations for the Stokes–Brinkman Equations as Homogenization Limit in Perforated Domains","authors":"Richard M. Höfer, Jonas Jansen","doi":"10.1007/s00205-024-01993-x","DOIUrl":"10.1007/s00205-024-01993-x","url":null,"abstract":"<div>We study the homogenization of the Dirichlet problem for the Stokes equations in (mathbb {R}^3) perforated by m spherical particles. We assume the positions and velocities of the particles to be identically and independently distributed random variables. In the critical regime, when the radii of the particles are of order (m^{-1}), the homogenization limit u is given as the solution to the Brinkman equations. We provide optimal rates for the convergence (u_m rightarrow u) in (L^2), namely (m^{-beta }) for all (beta < 1/2). Moreover, we consider the fluctuations. In the central limit scaling, we show that these converge to a Gaussian field, locally in (L^2(mathbb {R}^3)), with an explicit covariance. Our analysis is based on explicit approximations for the solutions (u_m) in terms of u as well as the particle positions and their velocities. These are shown to be accurate in (dot{H}^1(mathbb {R}^3)) to order (m^{-beta }) for all (beta < 1). Our results also apply to the analogous problem regarding the homogenization of the Poisson equations.</div>","PeriodicalId":55484,"journal":{"name":"Archive for Rational Mechanics and Analysis","volume":null,"pages":null},"PeriodicalIF":2.6,"publicationDate":"2024-05-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00205-024-01993-x.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141146773","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

Variational Worn Stones 变异磨损石

IF 2.6 1区数学

Archive for Rational Mechanics and Analysis Pub Date : 2024-05-20 DOI: 10.1007/s00205-024-01994-w

Graziano Crasta, Ilaria Fragalà

引用次数: 0

Asymptotic Stability of Couette Flow in a Strong Uniform Magnetic Field for the Euler-MHD System 欧拉-MHD 系统在强均匀磁场中耦合流的渐近稳定性

IF 2.6 1区数学

Archive for Rational Mechanics and Analysis Pub Date : 2024-05-17 DOI: 10.1007/s00205-024-01996-8

Weiren Zhao, Ruizhao Zi

{"title":"Asymptotic Stability of Couette Flow in a Strong Uniform Magnetic Field for the Euler-MHD System","authors":"Weiren Zhao, Ruizhao Zi","doi":"10.1007/s00205-024-01996-8","DOIUrl":"10.1007/s00205-024-01996-8","url":null,"abstract":"<div>In this paper, we prove the asymptotic stability of Couette flow in a strong uniform magnetic field for the Euler-MHD system, when the perturbations are in Gevrey-(frac{1}{s}), ((frac{1}{2}<sleqq 1)) and of size smaller than the resistivity coefficient (mu ). More precisely, we prove that <ol>\u0000 <li>\u0000 (1)\u0000 \u0000 the (mu ^{-frac{1}{3}})-amplification of the perturbed vorticity, namely, the size of the vorticity grows from (Vert omega _{textrm{in}}Vert _{mathcal {G}^{lambda _{0}}}lesssim mu ) to (Vert omega _{infty }Vert _{mathcal {G}^{lambda '}}lesssim mu ^{frac{2}{3}});\u0000 \u0000 </li>\u0000 <li>\u0000 (2)\u0000 \u0000 the polynomial decay of the perturbed current density, namely, (left| j_{ne }right| _{L^2}lesssim frac{c_0 }{langle trangle ^2 }min left{ mu ^{-frac{1}{3}},langle t rangle right} );\u0000 \u0000 </li>\u0000 <li>\u0000 (3)\u0000 \u0000 and the damping for the perturbed velocity and magnetic field, namely, <div><div>$$begin{aligned} left| (u^1_{ne },b^1_{ne })right| _{L^2}lesssim frac{c_0mu }{langle trangle }min left{ mu ^{-frac{1}{3}},langle t rangle right} , quad left| (u^2,b^2)right| _{L^2}lesssim frac{c_0mu }{langle trangle ^2 }min left{ mu ^{-frac{1}{3}},langle t rangle right} . end{aligned}$$</div></div>\u0000 \u0000 </li>\u0000 </ol> We also confirm that the strong uniform magnetic field stabilizes the Euler-MHD system near Couette flow.</div>","PeriodicalId":55484,"journal":{"name":"Archive for Rational Mechanics and Analysis","volume":null,"pages":null},"PeriodicalIF":2.6,"publicationDate":"2024-05-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141060126","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 Variational Perspective on Auxetic Metamaterials of Checkerboard-Type 棋盘式超材料的变量视角

IF 2.6 1区数学

Archive for Rational Mechanics and Analysis Pub Date : 2024-05-16 DOI: 10.1007/s00205-024-01989-7

Wolf-Patrick Düll, Dominik Engl, Carolin Kreisbeck

{"title":"A Variational Perspective on Auxetic Metamaterials of Checkerboard-Type","authors":"Wolf-Patrick Düll, Dominik Engl, Carolin Kreisbeck","doi":"10.1007/s00205-024-01989-7","DOIUrl":"10.1007/s00205-024-01989-7","url":null,"abstract":"<div>The main result of this work is a homogenization theorem via variational convergence for elastic materials with stiff checkerboard-type heterogeneities under the assumptions of physical growth and non-self-interpenetration. While the obtained energy estimates are rather standard, determining the effective deformation behavior, or in other words, characterizing the weak Sobolev limits of deformation maps whose gradients are locally close to rotations on the stiff components, is the challenging part. To this end, we establish an asymptotic rigidity result, showing that, under suitable scaling assumptions, the attainable macroscopic deformations are affine conformal contractions. This identifies the composite as a mechanical metamaterial with a negative Poisson’s ratio. Our proof strategy is to tackle first an idealized model with full rigidity on the stiff tiles to acquire insight into the mechanics of the model and then transfer the findings and methodology to the model with diverging elastic constants. The latter requires, in particular, a new quantitative geometric rigidity estimate for non-connected squares touching each other at their vertices and a tailored Poincaré type inequality for checkerboard structures.</div>","PeriodicalId":55484,"journal":{"name":"Archive for Rational Mechanics and Analysis","volume":null,"pages":null},"PeriodicalIF":2.6,"publicationDate":"2024-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00205-024-01989-7.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141060141","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

Regularity of the Optimal Sets for a Class of Integral Shape Functionals 一类积分形状函数最优集的规律性

IF 2.6 1区数学

Archive for Rational Mechanics and Analysis Pub Date : 2024-05-15 DOI: 10.1007/s00205-024-01984-y

Giuseppe Buttazzo, Francesco Paolo Maiale, Dario Mazzoleni, Giorgio Tortone, Bozhidar Velichkov

{"title":"Regularity of the Optimal Sets for a Class of Integral Shape Functionals","authors":"Giuseppe Buttazzo, Francesco Paolo Maiale, Dario Mazzoleni, Giorgio Tortone, Bozhidar Velichkov","doi":"10.1007/s00205-024-01984-y","DOIUrl":"10.1007/s00205-024-01984-y","url":null,"abstract":"<div>We prove the first regularity theorem for the free boundary of solutions to shape optimization problems involving integral functionals, for which the energy of a domain (Omega ) is obtained as the integral of a cost function j(u, x) depending on the solution u of a certain PDE problem on (Omega ). The main feature of these functionals is that the minimality of a domain (Omega ) cannot be translated into a variational problem for a single (real or vector valued) state function. In this paper we focus on the case of affine cost functions (j(u,x)=-g(x)u+Q(x)), where u is the solution of the PDE (-Delta u=f) with Dirichlet boundary conditions. We obtain the Lipschitz continuity and the non-degeneracy of the optimal u from the inwards/outwards optimality of (Omega ) and then we use the stability of (Omega ) with respect to variations with smooth vector fields in order to study the blow-up limits of the state function u. By performing a triple consecutive blow-up, we prove the existence of blow-up sequences converging to homogeneous stable solution of the one-phase Bernoulli problem and according to the blow-up limits, we decompose (partial Omega ) into a singular and a regular part. In order to estimate the Hausdorff dimension of the singular set of (partial Omega ) we give a new formulation of the notion of stability for the one-phase problem, which is preserved under blow-up limits and allows to develop a dimension reduction principle. Finally, by combining a higher order Boundary Harnack principle and a viscosity approach, we prove (C^infty ) regularity of the regular part of the free boundary when the data are smooth.</div>","PeriodicalId":55484,"journal":{"name":"Archive for Rational Mechanics and Analysis","volume":null,"pages":null},"PeriodicalIF":2.6,"publicationDate":"2024-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00205-024-01984-y.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140973999","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

Entropy and Thermodynamic Temperature in Nonequilibrium Classical Thermodynamics as Immediate Consequences of the Hahn–Banach Theorem: I. Existence 非平衡经典热力学中的熵和热力学温度作为哈恩-巴纳赫定理的直接后果：I. 存在

IF 2.6 1区数学

Archive for Rational Mechanics and Analysis Pub Date : 2024-05-15 DOI: 10.1007/s00205-024-01986-w

Martin Feinberg, Richard B. Lavine

引用次数: 0

Entropy and Thermodynamic Temperature in Nonequilibrium Classical Thermodynamics as Immediate Consequences of the Hahn–Banach Theorem: II Properties 哈恩-巴纳赫定理的直接后果--非平衡经典热力学中的熵和热力学温度：II 特性

IF 2.6 1区数学

Archive for Rational Mechanics and Analysis Pub Date : 2024-05-14 DOI: 10.1007/s00205-024-01987-9

Martin Feinberg, Richard B. Lavine

{"title":"Entropy and Thermodynamic Temperature in Nonequilibrium Classical Thermodynamics as Immediate Consequences of the Hahn–Banach Theorem: II Properties","authors":"Martin Feinberg, Richard B. Lavine","doi":"10.1007/s00205-024-01987-9","DOIUrl":"10.1007/s00205-024-01987-9","url":null,"abstract":"<div>In a companion article it was shown in a certain precise sense that, for any thermodynamical theory that respects the Kelvin–Planck second law, the Hahn–Banach theorem immediately ensures the existence of a pair of continuous functions of the local material state—a specific entropy (entropy per mass) and a thermodynamic temperature—that together satisfy the Clausius–Duhem inequality for every process. There was no requirement that the local states considered be states of equilibrium. This article addresses questions about properties of the entropy and thermodynamic temperature functions so obtained: To what extent do such temperature functions provide a faithful reflection of “hotness”? In precisely which Kelvin–Planck theories is such a temperature function essentially unique, and, among those theories, for which is the entropy function also essentially unique? What is a thermometer for a Kelvin–Planck theory, and, for the theory, what properties does the existence of a thermometer confer? In all of these questions, the Hahn–Banach Theorem again plays a crucial role.</div>","PeriodicalId":55484,"journal":{"name":"Archive for Rational Mechanics and Analysis","volume":null,"pages":null},"PeriodicalIF":2.6,"publicationDate":"2024-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00205-024-01987-9.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140940029","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

A Priori Estimates for Solutions to Landau Equation Under Prodi–Serrin Like Criteria 类似普罗迪-塞林标准下兰道方程解的先验估计值

IF 2.6 1区数学

Archive for Rational Mechanics and Analysis Pub Date : 2024-05-13 DOI: 10.1007/s00205-024-01992-y

R. Alonso, V. Bagland, L. Desvillettes, B. Lods

引用次数: 0