发布求助
文献互助 智能选刊 最新文献

Journal of Mathematical Fluid Mechanics最新文献

筛选
英文 中文
Wave breaking for the Fornberg-Whitham-Degasperis-Procesi equation Fornberg-Whitham-Degasperis-Procesi方程的破波
IF 1.3 3区 数学
Journal of Mathematical Fluid Mechanics Pub Date : 2026-04-28 DOI: 10.1007/s00021-026-01020-x
Runjie Han, Jian Li, Shaojie Yang
{"title":"Wave breaking for the Fornberg-Whitham-Degasperis-Procesi equation","authors":"Runjie Han,&nbsp;Jian Li,&nbsp;Shaojie Yang","doi":"10.1007/s00021-026-01020-x","DOIUrl":"10.1007/s00021-026-01020-x","url":null,"abstract":"<div><p>In this paper, we investigate wave breaking for the Fornberg-Whitham-Degasperis-Procesi equation which can be viewed as a special shallow water wave equation. Without any conservation laws, we give sufficient conditions on the initial data to lead to wave breaking.</p></div>","PeriodicalId":649,"journal":{"name":"Journal of Mathematical Fluid Mechanics","volume":"28 2","pages":""},"PeriodicalIF":1.3,"publicationDate":"2026-04-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147796330","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Well-Posedness of a Generalized Stokes Operator on Smooth Bounded Domains via Layer-Potentials 光滑有界域上基于层势的广义Stokes算子的适定性
IF 1.3 3区 数学
Journal of Mathematical Fluid Mechanics Pub Date : 2026-04-21 DOI: 10.1007/s00021-026-01021-w
Mirela Kohr, Victor Nistor, Wolfgang L. Wendland
{"title":"Well-Posedness of a Generalized Stokes Operator on Smooth Bounded Domains via Layer-Potentials","authors":"Mirela Kohr,&nbsp;Victor Nistor,&nbsp;Wolfgang L. Wendland","doi":"10.1007/s00021-026-01021-w","DOIUrl":"10.1007/s00021-026-01021-w","url":null,"abstract":"<div><p>We prove the invertibility of the relevant single and double layer potentials associated to some generalizations of the Stokes operator on bounded domains. In order to do that, we first develop an “algebra tool kit” to deal with limit and jump relations of layer operators. We do that first on <span>(mathbb {R}^{n})</span> for operators acting on a distribution supported on <span>({x_{n} = 0})</span> and then in general on (possibly non-compact) manifolds. We use these results to study the limit and jump relations of the layer potential operators associated to our generalized Stokes operators. As an application, we obtain well-posedness results for the Stokes system.</p></div>","PeriodicalId":649,"journal":{"name":"Journal of Mathematical Fluid Mechanics","volume":"28 2","pages":""},"PeriodicalIF":1.3,"publicationDate":"2026-04-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00021-026-01021-w.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147738338","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Velocity Optimization of Self-Equilibrated Obstacles in A Two-Dimensional Viscous Flow 二维粘性流动中自平衡障碍物的速度优化
IF 1.3 3区 数学
Journal of Mathematical Fluid Mechanics Pub Date : 2026-04-18 DOI: 10.1007/s00021-026-01017-6
Gilles A Francfort, Alessandro Giacomini, Scott Weady
{"title":"Velocity Optimization of Self-Equilibrated Obstacles in A Two-Dimensional Viscous Flow","authors":"Gilles A Francfort,&nbsp;Alessandro Giacomini,&nbsp;Scott Weady","doi":"10.1007/s00021-026-01017-6","DOIUrl":"10.1007/s00021-026-01017-6","url":null,"abstract":"<div><p>An obstacle is immersed in an externally driven 2D Stokes or Navier-Stokes fluid. We study the self-equilibration conditions for that obstacle under steady state assumptions on the flow. We then seek to optimize the translational and/or angular velocity of the obstacle by varying its shape. To allow general variations, we must consider a very large class of obstacles for which the notion of trace is meaningless. This forces us to revisit the notion of self-equilibration for both Stokes and Navier-Stokes in a measure theoretic environment.</p></div>","PeriodicalId":649,"journal":{"name":"Journal of Mathematical Fluid Mechanics","volume":"28 2","pages":""},"PeriodicalIF":1.3,"publicationDate":"2026-04-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147738111","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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 Estimate of Singular Set of Weak Solution to MHD Equations MHD方程弱解奇异集的估计
IF 1.3 3区 数学
Journal of Mathematical Fluid Mechanics Pub Date : 2026-04-13 DOI: 10.1007/s00021-026-01019-4
Zhong Tan, Jianfeng Zhou
{"title":"The Estimate of Singular Set of Weak Solution to MHD Equations","authors":"Zhong Tan,&nbsp;Jianfeng Zhou","doi":"10.1007/s00021-026-01019-4","DOIUrl":"10.1007/s00021-026-01019-4","url":null,"abstract":"<div><p>We are concerned with the estimate of singular set of weak solution to Magneto-hydrodynamical (MHD) equations. First, we show that if the pressure <i>P</i> associated to a Leray-Hopf weak solution (<i>u</i>, <i>b</i>) satisfies some additional assumptions, then there is a reduction in the Hausdorff dimension of singular set at a first potential blow up time. Next, instead of imposing the assumption on the pressure, we prove that if the initial data satisfies an extra assumption, then (<i>u</i>, <i>b</i>) possess finite number singular points at first potential blow up time.</p></div>","PeriodicalId":649,"journal":{"name":"Journal of Mathematical Fluid Mechanics","volume":"28 2","pages":""},"PeriodicalIF":1.3,"publicationDate":"2026-04-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147737526","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Standing Wave Solutions of abcd-systems for Water Waves 水波abcd-系统的驻波解
IF 1.3 3区 数学
Journal of Mathematical Fluid Mechanics Pub Date : 2026-04-11 DOI: 10.1007/s00021-026-01013-w
Peifei Song, Yuhao Xie, Min Chen, Shenghao Li
{"title":"Standing Wave Solutions of abcd-systems for Water Waves","authors":"Peifei Song,&nbsp;Yuhao Xie,&nbsp;Min Chen,&nbsp;Shenghao Li","doi":"10.1007/s00021-026-01013-w","DOIUrl":"10.1007/s00021-026-01013-w","url":null,"abstract":"<div><p>We continue the study for standing wave solutions of <i>abcd</i>-systems which was started by Chen and Iooss (Chen, M., Iooss, G.: <i>Eur. J. Mech. B, Fluids</i>, 24(1):113–124, 2005) for the BBM system via the Lyapunov-Schmidt method. In this paper, we will first discuss the feasibility of the Lyapunov-Schmidt method for bifurcating standing wave solutions of <i>abcd</i>-systems. These systems will be characterized into three categories: feasible, infeasible and uncertain feasible ones. In particular, we prove the existence of nontrivial bifurcating standing waves for the Bona-Smith system.</p></div>","PeriodicalId":649,"journal":{"name":"Journal of Mathematical Fluid Mechanics","volume":"28 2","pages":""},"PeriodicalIF":1.3,"publicationDate":"2026-04-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147737505","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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-Uniqueness and BV Blowup for Vacuously Liu-Admissible Solutions to P-System Via Computer-Assisted Proof 用计算机辅助证明p -系统真空刘容许解的非唯一性和BV爆破
IF 1.3 3区 数学
Journal of Mathematical Fluid Mechanics Pub Date : 2026-04-10 DOI: 10.1007/s00021-026-01018-5
Sam G. Krupa
{"title":"Non-Uniqueness and BV Blowup for Vacuously Liu-Admissible Solutions to P-System Via Computer-Assisted Proof","authors":"Sam G. Krupa","doi":"10.1007/s00021-026-01018-5","DOIUrl":"10.1007/s00021-026-01018-5","url":null,"abstract":"<div><p>In this paper, we consider non-uniqueness and finite time blowup of the BV-norm for exact solutions to genuinely nonlinear hyperbolic systems in one space dimension, in particular the <i>p</i>-system. The recent Bressan-De Lellis result [<i>Arch. Ration. Mech. Anal.</i>, 247(6):Paper No. 106, 12, 2023] shows that whenever a BV solution exists, with finite (but possibly very large total variation), it is unique if each shock verifies the Liu <i>E</i>-condition. We show non-uniqueness of solutions by convex integration. The solutions we construct are Liu-admissible for a trivial reason: there are no shocks, so the Liu <i>E</i>-condition is vacuously satisfied. But our construction shows exactly that there is an issue, a qualitative difference between small data solutions (for example in the BV class) and large data solutions, where this exact type of phenomenon might occur. Our result can be interpreted as a cautionary example to show that the Liu <i>E</i>-condition is satisfactory for small oscillations but <i>not for large oscillations</i> where typically these type of constructions appear. In particular, we present Riemann initial data which admits infinitely many bounded solutions, each of which experience, not just finite time, but in fact <i>instantaneous</i> blowup of the BV norm. The Riemann initial data is allowed to come from an open set in state space. Our method provably does not admit the natural strictly convex entropy. The proof of our theorem is computer-assisted. Our code is available on the GitHub.</p></div>","PeriodicalId":649,"journal":{"name":"Journal of Mathematical Fluid Mechanics","volume":"28 2","pages":""},"PeriodicalIF":1.3,"publicationDate":"2026-04-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147643168","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Existence of All Wilton Ripples of the Kawahara Equation Kawahara方程的所有Wilton波纹的存在性
IF 1.3 3区 数学
Journal of Mathematical Fluid Mechanics Pub Date : 2026-04-08 DOI: 10.1007/s00021-026-01014-9
Ryan P. Creedon
{"title":"Existence of All Wilton Ripples of the Kawahara Equation","authors":"Ryan P. Creedon","doi":"10.1007/s00021-026-01014-9","DOIUrl":"10.1007/s00021-026-01014-9","url":null,"abstract":"<div><p>We investigate the existence of Wilton ripple solutions of the Kawahara equation. Without loss of generality, these are <span>(2pi )</span>-periodic, traveling-wave solutions whose profiles at zero amplitude have a codimension-1 bifurcation from a linear combination of <span>(cos (x))</span> and <span>(cos (Kx))</span> for <span>(K in mathbb {N} setminus {1})</span>. Using a Lyapunov-Schmidt reduction, we prove the existence of these solutions for all <i>K</i>, in contrast to previous work demonstrating existence only for <span>(K = 2)</span>. Although the proof holds only for the Kawahara equation, many ideas introduced in the proof can be applied to more general contexts, including Wilton ripples of the gravity-capillary water wave equations.</p></div>","PeriodicalId":649,"journal":{"name":"Journal of Mathematical Fluid Mechanics","volume":"28 2","pages":""},"PeriodicalIF":1.3,"publicationDate":"2026-04-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147642661","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Solution Formula and (H^2)-Solvability for the Stokes System in An Infinite Layer with Upper Stress-Free and Lower Slip-Type Boundary Conditions 具有上无应力和下滑移型边界条件的无限层Stokes系统的解公式和(H^2) -可解性
IF 1.3 3区 数学
Journal of Mathematical Fluid Mechanics Pub Date : 2026-04-08 DOI: 10.1007/s00021-026-01015-8
Daisuke Hirata
{"title":"Solution Formula and (H^2)-Solvability for the Stokes System in An Infinite Layer with Upper Stress-Free and Lower Slip-Type Boundary Conditions","authors":"Daisuke Hirata","doi":"10.1007/s00021-026-01015-8","DOIUrl":"10.1007/s00021-026-01015-8","url":null,"abstract":"<div><p>In this paper, we study the initial-boundary value problem for the Stokes system in the three-dimensional infinite layer domain <span>(Omega = (0,frac{pi }{2}) times mathbb {R}^2)</span>, subject to upper stress-free and lower slip-type boundary conditions. Using the Fourier method, we derive an integral formulation for regular solutions. Based on this formula, we demonstrate the solvability of the problem in the <span>(L^2)</span>-based Sobolev space <span>(H^2(Omega ))</span>.</p></div>","PeriodicalId":649,"journal":{"name":"Journal of Mathematical Fluid Mechanics","volume":"28 2","pages":""},"PeriodicalIF":1.3,"publicationDate":"2026-04-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147642774","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Spatial Pointwise Behavior of Gradient of Navier-Stokes Flow Around a Rigid Body Moving by Time-Periodic Motion, with Applications to Stability/attainability of time-periodic Flow 时间周期运动刚体周围Navier-Stokes流动梯度的空间点态行为及其在时间周期流动稳定性/可达性中的应用
IF 1.3 3区 数学
Journal of Mathematical Fluid Mechanics Pub Date : 2026-04-03 DOI: 10.1007/s00021-026-01016-7
Tomoki Takahashi
{"title":"Spatial Pointwise Behavior of Gradient of Navier-Stokes Flow Around a Rigid Body Moving by Time-Periodic Motion, with Applications to Stability/attainability of time-periodic Flow","authors":"Tomoki Takahashi","doi":"10.1007/s00021-026-01016-7","DOIUrl":"10.1007/s00021-026-01016-7","url":null,"abstract":"<div><p>Let us consider the spatial pointwise behavior of time-periodic solutions to the Navier-Stokes equation in the exterior of a rigid body, moving by time-periodic motion. For the translational and angular velocity of the body, assuming besides smallness and regularity, either of the following conditions: (i) translation or rotation is absent; (ii) both velocities are parallel to the same constant vector. If time average over a period of translational velocity, <span>(lambda )</span> (say), is non-zero (resp. zero), we then show that gradient of the velocity of the fluid decays like the one of the gradient of the Oseen fundamental solution (resp. decays at the rate <span>(O(|x|^{-2}))</span>). As applications, in the case <span>(lambda =0)</span>, we show the attainability of the time-periodic solution for small data. In the case <span>(lambda ne 0)</span>, the stability/attainability of the time-periodic solution with sharp decay properties are also deduced.</p></div>","PeriodicalId":649,"journal":{"name":"Journal of Mathematical Fluid Mechanics","volume":"28 2","pages":""},"PeriodicalIF":1.3,"publicationDate":"2026-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00021-026-01016-7.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147606803","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Convergence of a Second-Order Projection Method to Leray-Hopf Solutions of the Incompressible Navier-Stokes Equations 不可压缩Navier-Stokes方程Leray-Hopf解的二阶投影法的收敛性
IF 1.3 3区 数学
Journal of Mathematical Fluid Mechanics Pub Date : 2026-03-19 DOI: 10.1007/s00021-025-00985-5
Franziska Weber
{"title":"Convergence of a Second-Order Projection Method to Leray-Hopf Solutions of the Incompressible Navier-Stokes Equations","authors":"Franziska Weber","doi":"10.1007/s00021-025-00985-5","DOIUrl":"10.1007/s00021-025-00985-5","url":null,"abstract":"<div><p>We analyze a second-order projection method for the incompressible Navier-Stokes equations on bounded Lipschitz domains. The scheme employs a Backward Differentiation Formula of order two (BDF2) for the time discretization, combined with conforming finite elements in space. Projection methods are widely used to enforce incompressibility, yet rigorous convergence results for possibly non-smooth solutions have so far been restricted to first-order schemes. We establish, for the first time, convergence (up to subsequence) of a second-order projection method to Leray–Hopf weak solutions under minimal assumptions on the data, namely <span>(u_0 in L^2_{textrm{div}}(Omega ))</span> and <span>(f in L^2(0,T;L^2_{textrm{div}}(Omega )))</span>. Our analysis relies on two ingredients: A discrete energy inequality providing uniform <span>(L^infty (0,T;L^2(Omega )))</span> and <span>(L^2(0,T;H^1_0(Omega )))</span> bounds for suitable interpolants of the discrete velocities, and a compactness argument combining Simon’s theorem with refined time-continuity estimates. These tools overcome the difficulty that only the projected velocity satisfies an approximate divergence-free condition, while the intermediate velocity is controlled in space. We conclude that a subsequence of the approximations converges to a Leray–Hopf weak solution. This result provides the first rigorous convergence proof for a higher-order projection method under no additional assumptions on the solution beyond those following from the standard a priori energy estimate.</p></div>","PeriodicalId":649,"journal":{"name":"Journal of Mathematical Fluid Mechanics","volume":"28 2","pages":""},"PeriodicalIF":1.3,"publicationDate":"2026-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00021-025-00985-5.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147559770","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
下一页 尾页
0
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整，为了账户安全，请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
请完成安全验证×
相关产品
×
本文献相关产品
联系我们：info@booksci.cn Book学术提供免费学术资源搜索服务，方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号：604180095
Book学术官方微信
小红书