Journal of Mathematical Fluid Mechanics最新文献_第5页

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

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

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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>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 p-system. The recent Bressan-De Lellis result [Arch. Ration. Mech. Anal., 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 E-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 E-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 E-condition is satisfactory for small oscillations but not for large oscillations 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 instantaneous 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.</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

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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

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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

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>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 (u_0 in L^2_{textrm{div}}(Omega )) and (f in L^2(0,T;L^2_{textrm{div}}(Omega ))). Our analysis relies on two ingredients: A discrete energy inequality providing uniform (L^infty (0,T;L^2(Omega ))) and (L^2(0,T;H^1_0(Omega ))) 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.</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

Asymptotic Stability of Composite Waves of Two Viscous Shocks for Relaxed Compressible Navier-Stokes Equations 松弛可压缩Navier-Stokes方程下两粘性激波的渐近稳定性

IF 1.3 3区数学

Journal of Mathematical Fluid Mechanics Pub Date : 2026-03-19 DOI: 10.1007/s00021-026-01010-z

Renyong Guan, Yuxi Hu

引用次数: 0

Global Small-Time Approximate Null and Lagrangian Controllability of the Viscous Non-Resistive MHD System in a 3 D Domain with Navier Type Boundary Conditions 三维Navier型边界条件下粘性非电阻MHD系统的全局小时近似零值和拉格朗日可控性

IF 1.3 3区数学

Journal of Mathematical Fluid Mechanics Pub Date : 2026-03-10 DOI: 10.1007/s00021-026-01012-x

Jiajiang Liao, Franck Sueur, Ping Zhang

{"title":"Global Small-Time Approximate Null and Lagrangian Controllability of the Viscous Non-Resistive MHD System in a 3 D Domain with Navier Type Boundary Conditions","authors":"Jiajiang Liao, Franck Sueur, Ping Zhang","doi":"10.1007/s00021-026-01012-x","DOIUrl":"10.1007/s00021-026-01012-x","url":null,"abstract":"<div>We consider the incompressible viscous MHD system without magnetic diffusion in a 3D bounded domain with Navier type boundary condition. We establish the global small-time approximate null controllability and the Lagrangian controllability of the system, in the class of smooth solutions, by following the approach initiated in [7] to establish the global small-time null controllability of the incompressible Navier-Stokes equations in the class of weak solutions and extended in [34] to establish the global small-time null and Lagrangian controllability of the incompressible Navier-Stokes equations in the class of strong solutions. This approach makes use of controls with an extra fast scale in time and some corresponding multi-scale asymptotic expansions of the controlled solution. This expansion is constructed by an iterative process which requires some regularity. The extra-difficulty here is that the MHD system at stake is mixed hyperbolic-parabolic, without any regularizing effect on the magnetic field. Although our strategy makes use of a quite precise asymptotic expansion, we succeed to cover the case where the initial velocity belongs the Sobolev space (H^{24}) and the initial magnetic field belongs to the Sobolev space (H^8).</div>","PeriodicalId":649,"journal":{"name":"Journal of Mathematical Fluid Mechanics","volume":"28 2","pages":""},"PeriodicalIF":1.3,"publicationDate":"2026-03-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147441137","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

Revisiting the Slip Boundary Condition: Surface Roughness as a Hidden Tuning Parameter 重新审视滑移边界条件：表面粗糙度作为一个隐藏的调谐参数

IF 1.3 3区数学

Journal of Mathematical Fluid Mechanics Pub Date : 2026-03-04 DOI: 10.1007/s00021-026-01009-6

Matthias Maier, Peter Munch, Murtazo Nazarov

{"title":"Revisiting the Slip Boundary Condition: Surface Roughness as a Hidden Tuning Parameter","authors":"Matthias Maier, Peter Munch, Murtazo Nazarov","doi":"10.1007/s00021-026-01009-6","DOIUrl":"10.1007/s00021-026-01009-6","url":null,"abstract":"<div>In this paper, we investigate the effect of boundary surface roughness on numerical simulations of incompressible fluid flow past a cylinder in two and three spatial dimensions furnished with slip boundary conditions. The governing equations are approximated using a continuous finite element method, stabilized with a Galerkin least-squares approach. Through a series of numerical experiments, we demonstrate that: (i) the introduction of surface roughness through numerical discretization error, or mesh distortion, makes the potential flow solution unstable; (ii) when numerical surface roughness and mesh distortion are minimized by using high-order isoparametric geometry mappings, a stable potential flow is obtained in both two and three dimensions; (iii) numerical surface roughness, mesh distortion and refinement level can be used as control parameters to manipulate drag and lift forces resulting in numerical values spanning more than an order of magnitude. Our results cast some doubt on the predictive capability of the slip boundary condition for wall modeling in turbulent simulations of incompressible flow.</div>","PeriodicalId":649,"journal":{"name":"Journal of Mathematical Fluid Mechanics","volume":"28 2","pages":""},"PeriodicalIF":1.3,"publicationDate":"2026-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00021-026-01009-6.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147362897","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