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3-d Shock-Free Compressible Euler Flows with Amplitude Blowup and Pile-Up of Characteristics 具有振幅放大和堆积特性的三维无激波可压缩欧拉流
IF 2.9 1区 数学
Archive for Rational Mechanics and Analysis Pub Date : 2026-10-16 DOI: 10.1007/s00205-026-02260-x
Helge Kristian Jenssen
{"title":"3-d Shock-Free Compressible Euler Flows with Amplitude Blowup and Pile-Up of Characteristics","authors":"Helge Kristian Jenssen","doi":"10.1007/s00205-026-02260-x","DOIUrl":"10.1007/s00205-026-02260-x","url":null,"abstract":"<div><p>Recent works have demonstrated that self-similar radial Euler flows of an ideal polytropic gas in 2 and 3 dimensions can drive primary (non-differentiated) flow variables to infinity at the center of motion. Unsurprisingly, this type of behavior can generate an outgoing shock wave from the point of collapse. In this work we prove that there is an alternative scenario possible in 3-d flow: an incoming, radial <span>(C^1)</span> flow suffers blowup at a single point, including in density and pressure, and yet remains <span>(C^1)</span> beyond collapse. No shock is generated despite the fact that the density gradient <span>(nabla _{{textbf{x}}}rho )</span>, as well as the density of characteristics, becomes unbounded at the center of motion at time of blowup. Furthermore, we verify that this behavior is possible even in cases where the fluid is everywhere moving toward the center of motion at time of collapse, in which case also <span>({{,textrm{div},}}_{{textbf{x}}}{textbf{u}}rightarrow -infty )</span>. These phenomena underscore the subtlety of shock formation in multi-d flow.</p></div>","PeriodicalId":55484,"journal":{"name":"Archive for Rational Mechanics and Analysis","volume":"250 6","pages":""},"PeriodicalIF":2.9,"publicationDate":"2026-10-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149189733","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
Correction to: “Global Weak Solutions to a Diffuse Interface Model for Incompressible Two-Phase Flows with Moving Contact Lines and Different Densities” 修正：“具有移动接触线和不同密度的不可压缩两相流扩散界面模型的整体弱解”
IF 2.9 1区 数学
Archive for Rational Mechanics and Analysis Pub Date : 2026-10-06 DOI: 10.1007/s00205-026-02254-9
Ciprian G. Gal, Maurizio Grasselli, Hao Wu
{"title":"Correction to: “Global Weak Solutions to a Diffuse Interface Model for Incompressible Two-Phase Flows with Moving Contact Lines and Different Densities”","authors":"Ciprian G. Gal,&nbsp;Maurizio Grasselli,&nbsp;Hao Wu","doi":"10.1007/s00205-026-02254-9","DOIUrl":"10.1007/s00205-026-02254-9","url":null,"abstract":"","PeriodicalId":55484,"journal":{"name":"Archive for Rational Mechanics and Analysis","volume":"250 6","pages":""},"PeriodicalIF":2.9,"publicationDate":"2026-10-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149098239","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
Homogenization of Non-symmetric Convolution Type Operators 非对称卷积型算子的均匀化
IF 2.9 1区 数学
Archive for Rational Mechanics and Analysis Pub Date : 2026-10-06 DOI: 10.1007/s00205-026-02249-6
Andrey Piatnitski, Vladimir Sloushch, Tatiana Suslina, Elena Zhizhina
{"title":"Homogenization of Non-symmetric Convolution Type Operators","authors":"Andrey Piatnitski,&nbsp;Vladimir Sloushch,&nbsp;Tatiana Suslina,&nbsp;Elena Zhizhina","doi":"10.1007/s00205-026-02249-6","DOIUrl":"10.1007/s00205-026-02249-6","url":null,"abstract":"<div><p>The paper studies homogenization problem for a bounded in <span>(L_2(mathbb {R}^d))</span> convolution type operator <span>({mathbb {A}}_varepsilon )</span>, <span>(varepsilon &gt;0)</span>, of the form </p><div><div><span>$$begin{aligned} ({mathbb {A}}_varepsilon u) ({textbf{x}}) = varepsilon ^{-d-2} int _{mathbb {R}^d} a(({textbf{x}}-{textbf{y}})/varepsilon ) mu ({textbf{x}}/varepsilon , {textbf{y}}/varepsilon ) left( u({textbf{x}}) - u({textbf{y}}) right) ,d{textbf{y}}. end{aligned}$$</span></div></div><p>It is assumed that <span>(a({textbf{x}}))</span> is a non-negative function from <span>(L_1(mathbb {R}^d))</span>, and <span>(mu ({textbf{x}},{textbf{y}}))</span> is a periodic in <span>({textbf{x}})</span> and <span>({textbf{y}})</span> function such that <span>(0&lt; mu _- leqslant mu ({textbf{x}},{textbf{y}}) leqslant mu _+&lt; infty )</span>. No symmetry assumption on <span>(a(cdot ))</span> and <span>(mu (cdot ))</span> is imposed, so the operator <span>({mathbb {A}}_varepsilon )</span> need not be self-adjoint. Under the assumption that the moments <span>(M_k = int _{mathbb {R}^d} |{textbf{x}}|^k a({textbf{x}}),d{textbf{x}})</span>, <span>(k=1,2,3)</span>, are finite we obtain, for small <span>(varepsilon &gt;0)</span>, sharp in order approximation of the resolvent <span>(({mathbb {A}}_varepsilon + I)^{-1})</span> in the operator norm in <span>(L_2(mathbb {R}^d))</span>, the discrepancy being of order <span>(O(varepsilon ))</span>. The approximation is given by an operator of the form <span>(({mathbb {A}}^0 + varepsilon ^{-1} langle varvec{alpha },nabla rangle + I)^{-1})</span> multiplied on the right by a periodic function <span>(q_0({textbf{x}}/varepsilon ))</span>; here <span>({mathbb {A}}^0 = - operatorname {div}g^0 nabla )</span> is the effective operator, and <span>(varvec{alpha })</span> is a constant vector.</p></div>","PeriodicalId":55484,"journal":{"name":"Archive for Rational Mechanics and Analysis","volume":"250 6","pages":""},"PeriodicalIF":2.9,"publicationDate":"2026-10-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00205-026-02249-6.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149098241","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 Subsequentially Fast Dynamo on (mathbb {T}^3) 随后快速发电机打开 (mathbb {T}^3)
IF 2.9 1区 数学
Archive for Rational Mechanics and Analysis Pub Date : 2026-10-06 DOI: 10.1007/s00205-026-02255-8
Keefer Rowan
{"title":"A Subsequentially Fast Dynamo on (mathbb {T}^3)","authors":"Keefer Rowan","doi":"10.1007/s00205-026-02255-8","DOIUrl":"10.1007/s00205-026-02255-8","url":null,"abstract":"<div><p>We construct a smooth velocity field <i>u</i> on <span>(mathbb {R}_+ times mathbb {T}^3)</span> that exhibits kinematic dynamo action, causing exponential growth in solutions to the magnetohydrodynamic induction equation, uniformly over a suitable sequence of diffusivities <span>(kappa _j rightarrow 0)</span> and times <span>(t^j_ell {mathop {rightarrow }limits ^{ell rightarrow infty }} infty )</span>. We call this a subsequentially fast dynamo.</p></div>","PeriodicalId":55484,"journal":{"name":"Archive for Rational Mechanics and Analysis","volume":"250 6","pages":""},"PeriodicalIF":2.9,"publicationDate":"2026-10-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149098240","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
Rigorous Analysis of Shape Transitions in Frustrated Elastic Ribbons 受挫弹性带形状转变的严格分析
IF 2.9 1区 数学
Archive for Rational Mechanics and Analysis Pub Date : 2026-10-03 DOI: 10.1007/s00205-026-02250-z
Cy Maor, Maria Giovanna Mora
{"title":"Rigorous Analysis of Shape Transitions in Frustrated Elastic Ribbons","authors":"Cy Maor,&nbsp;Maria Giovanna Mora","doi":"10.1007/s00205-026-02250-z","DOIUrl":"10.1007/s00205-026-02250-z","url":null,"abstract":"<div><p>Ribbons are elastic bodies of thickness <i>t</i> and width <i>w</i> with <span>(tll wll 1)</span> (after appropriate nondimensionalization). Many ribbons in nature have a non-trivial internal geometry, making them incompatible with Euclidean space. This incompatibility—expressed mathematically as a failure of the Gauss–Codazzi equations for surfaces—can trigger shape transitions between narrow and wide ribbons. These transitions depend on the internal geometry: ribbons whose incompatibility arises from failure of the Gauss equation always exhibit a transition, whereas those whose incompatibility arises from failure of the Codazzi equations may or may not. We give the first rigorous analysis of this phenomenon, mainly for ribbons whose first fundamental form is flat. For Gauss-incompatible ribbons we identify the natural energy scaling of the problem and prove the existence of a shape transition. For Codazzi-incompatible ribbons we give a necessary condition for a transition to occur. Furthermore, our study reveals a fundamental distinction: the transition is “microscopic” for Gauss-incompatible ribbons, persisting as the width tends to 0, whereas it is “mesoscopic” for Codazzi-incompatible ribbons, observable only at small but finite width. The results are obtained by calculating the <span>(Gamma )</span>-limits, as <span>(t,wrightarrow 0)</span>, for narrow ribbons (<span>(w^2 ll t)</span>), and wide ribbons (taking <i>t</i> to zero and then <i>w</i>), in the natural energy scalings dictated by the internal geometry.</p></div>","PeriodicalId":55484,"journal":{"name":"Archive for Rational Mechanics and Analysis","volume":"250 6","pages":""},"PeriodicalIF":2.9,"publicationDate":"2026-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00205-026-02250-z.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149098100","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
Unstable Vortices, Sharp Non-Uniqueness with Forcing, and Global Smooth Solutions for the SQG Equation 不稳定涡、带强迫的尖锐非唯一性及SQG方程的全局光滑解
IF 2.9 1区 数学
Archive for Rational Mechanics and Analysis Pub Date : 2026-10-03 DOI: 10.1007/s00205-026-02252-x
Ángel Castro, Daniel Faraco, Francisco Mengual, Marcos Solera
{"title":"Unstable Vortices, Sharp Non-Uniqueness with Forcing, and Global Smooth Solutions for the SQG Equation","authors":"Ángel Castro,&nbsp;Daniel Faraco,&nbsp;Francisco Mengual,&nbsp;Marcos Solera","doi":"10.1007/s00205-026-02252-x","DOIUrl":"10.1007/s00205-026-02252-x","url":null,"abstract":"<div><p>We prove that non-uniqueness of weak solutions to the forced <span>(alpha )</span>-SQG equation with Sobolev regularity <span>(W^{s,p})</span> in the supercritical regime <span>(s &lt; alpha + frac{2}{p})</span>, covering the 2D Euler equation (<span>(alpha = 0)</span>), the Surface Quasi-Geostrophic equation (<span>(alpha = 1)</span>), and the intermediate cases. A key step is the construction of smooth, compactly supported vortices that exhibit non-linear instability. As a by-product, we show that existence of global smooth solutions to the (unforced) <span>(alpha )</span>-SQG equation that are neither rotating nor traveling.</p></div>","PeriodicalId":55484,"journal":{"name":"Archive for Rational Mechanics and Analysis","volume":"250 6","pages":""},"PeriodicalIF":2.9,"publicationDate":"2026-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00205-026-02252-x.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149098098","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
Intermittency and Dissipation Regularity in Turbulence 湍流中的间歇性和耗散规律
IF 2.9 1区 数学
Archive for Rational Mechanics and Analysis Pub Date : 2026-10-01 DOI: 10.1007/s00205-026-02245-w
Luigi De Rosa, Theodore D. Drivas, Marco Inversi, Philip Isett
{"title":"Intermittency and Dissipation Regularity in Turbulence","authors":"Luigi De Rosa,&nbsp;Theodore D. Drivas,&nbsp;Marco Inversi,&nbsp;Philip Isett","doi":"10.1007/s00205-026-02245-w","DOIUrl":"10.1007/s00205-026-02245-w","url":null,"abstract":"<div><p>We lay down a geometric-analytic framework to capture properties of energy dissipation within weak solutions to the incompressible Euler equations. For solutions with spatial Besov regularity, it is proven that the Duchon–Robert distribution has optimal improved regularity in a negative Besov space and, in the case it is a Radon measure, it is absolutely continuous with respect to a suitable Hausdorff measure. This imposes quantitative constraints on the dimension of the, possibly fractal, dissipative set and the admissible structure functions exponents, relating to the phenomenon of “intermittency” in turbulence. As a by-product of the approach, we also recover many known “Onsager singularity” type results.</p></div>","PeriodicalId":55484,"journal":{"name":"Archive for Rational Mechanics and Analysis","volume":"250 5","pages":""},"PeriodicalIF":2.9,"publicationDate":"2026-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149132323","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
Non-linear Stability of Shock Profiles in Dissipative Hyperbolic–Hyperbolic Systems 耗散双曲-双曲系统激波剖面的非线性稳定性
IF 2.9 1区 数学
Archive for Rational Mechanics and Analysis Pub Date : 2026-09-27 DOI: 10.1007/s00205-026-02247-8
Matthias Sroczinski, Kevin Zumbrun
{"title":"Non-linear Stability of Shock Profiles in Dissipative Hyperbolic–Hyperbolic Systems","authors":"Matthias Sroczinski,&nbsp;Kevin Zumbrun","doi":"10.1007/s00205-026-02247-8","DOIUrl":"10.1007/s00205-026-02247-8","url":null,"abstract":"<div><p>We give the first proof of nonlinear stability for smooth shock profiles of second-order dissipative hyperbolic-hyperbolic systems under the assumption of spectral stability, showing stability of smooth small-amplitude profiles in dimensions greater than or equal to two. This class of systems notably includes the two types of causal viscous relativistic gas models introduced respectively by Freistühler–Temple and Bemfica–Disconzi–Noronha, and (the equivalent second-order form of) a class of first-order numerical relaxation systems generalizing the well-known Jin-Xin relaxation schemes. A significant technical innovation is a new para-differential type of nonlinear damping estimate similar to that used by the first author to study stability of constant states, allowing the treatment of systems far from the symmetric structure required for the standard “Kawashima-type” energy estimates that are typically used for that purpose.</p></div>","PeriodicalId":55484,"journal":{"name":"Archive for Rational Mechanics and Analysis","volume":"250 5","pages":""},"PeriodicalIF":2.9,"publicationDate":"2026-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149133030","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
On the Uniqueness and Structural Stability of Couette-Poiseuille Flow in a Channel for Arbitrary Values of the Flux 流量为任意值时通道内库埃-泊泽维尔流的唯一性和结构稳定性
IF 2.9 1区 数学
Archive for Rational Mechanics and Analysis Pub Date : 2026-09-27 DOI: 10.1007/s00205-026-02246-9
Giovanni P. Galdi, Filippo Gazzola, Mikhail Korobkov, Xiao Ren, Gianmarco Sperone
{"title":"On the Uniqueness and Structural Stability of Couette-Poiseuille Flow in a Channel for Arbitrary Values of the Flux","authors":"Giovanni P. Galdi,&nbsp;Filippo Gazzola,&nbsp;Mikhail Korobkov,&nbsp;Xiao Ren,&nbsp;Gianmarco Sperone","doi":"10.1007/s00205-026-02246-9","DOIUrl":"10.1007/s00205-026-02246-9","url":null,"abstract":"<div><p>We establish the uniqueness and structural stability of a class of parallel flows in a 2D straight, infinite channel, under perturbations with either globally or locally bounded Dirichlet integrals. The significant feature of our result is that it does not require any restriction on the size of the flux characterizing the flow. More precisely, by extending and refining an approach initially introduced by J.B. McLeod, we demonstrate the continuous invertibility of the linearized operator at a generic Couette-Poiseuille solution that does not exhibit flow reversal. We then deduce local uniqueness of these solutions as well as their nonlinear structural stability under small external forces. Moreover, we prove the uniqueness of certain class of Couette-Poiseuille solutions “in the large”, within the set of solutions possessing natural symmetry. Finally, we bring an example showing that, in general, if the flow reversal assumption is violated, the linearized operator is no longer invertible.</p></div>","PeriodicalId":55484,"journal":{"name":"Archive for Rational Mechanics and Analysis","volume":"250 5","pages":""},"PeriodicalIF":2.9,"publicationDate":"2026-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149132534","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
Global Well-Posedness for the One-Phase Muskat Problem in 3D 三维单相Muskat问题的全局适定性
IF 2.9 1区 数学
Archive for Rational Mechanics and Analysis Pub Date : 2026-09-23 DOI: 10.1007/s00205-026-02240-1
Hongjie Dong, Francisco Gancedo, Huy Q. Nguyen
{"title":"Global Well-Posedness for the One-Phase Muskat Problem in 3D","authors":"Hongjie Dong,&nbsp;Francisco Gancedo,&nbsp;Huy Q. Nguyen","doi":"10.1007/s00205-026-02240-1","DOIUrl":"10.1007/s00205-026-02240-1","url":null,"abstract":"<div><p>This paper is concerned with the long time dynamics of the free boundary of a Darcy fluid in three space dimensions, also known as the one-phase Muskat problem. The dynamics of the free boundary is governed by a nonlocal fully nonlinear parabolic partial differential equation. It is proven that for any periodic Lipschitz graph given as initial data, the problem has a unique global-in-time solution which satisfies the equation in the strong sense. Moreover, all Hölder norms of the solution decay exponentially in time. These results have been previously established in two space dimensions. This paper addresses new challenges to extend the results to the more difficult three dimensional setting. The approach developed is critical in three space dimensions and crucially relies on Dahlberg–Kenig’s <span>(W^{1, 2+varepsilon })</span> optimal regularity for layer potentials together with delicate structures of the Dirichlet-to-Neumann operator and layer potentials in Lipschitz domains of <span>(mathbb {T}^2times mathbb {R})</span>.</p></div>","PeriodicalId":55484,"journal":{"name":"Archive for Rational Mechanics and Analysis","volume":"250 5","pages":""},"PeriodicalIF":2.9,"publicationDate":"2026-09-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149034568","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
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