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Stability of the Couette Flow for 2D Boussinesq Equations with Only Vertical Dissipation 仅考虑垂直耗散的二维Boussinesq方程的Couette流的稳定性
IF 1.3 3区 数学
Journal of Mathematical Fluid Mechanics Pub Date : 2025-10-22 DOI: 10.1007/s00021-025-00978-4
Qian Li, Wen Luo, Zekai Luo
{"title":"Stability of the Couette Flow for 2D Boussinesq Equations with Only Vertical Dissipation","authors":"Qian Li,&nbsp;Wen Luo,&nbsp;Zekai Luo","doi":"10.1007/s00021-025-00978-4","DOIUrl":"10.1007/s00021-025-00978-4","url":null,"abstract":"<div><p>In this article, we investigate the nonlinear stability of the Couette flow under the Boussinesq equations with only vertical dissipation in <span>({mathbb {T}}times {mathbb {R}})</span>. Inspired by the work of Wei and Zhang [Tunis. J. Math. 5(3):573-592 (2023)] and taking into account perturbations with different sizes, we can address the influence of buoyancy term within the coupled system. We obtain a stability result under the initial perturbations condition: <span>(Vert omega ^{(0)}Vert _{H^b}+nu ^{-1/2}Vert theta ^{(0)}Vert _{H^b}+nu ^{-1/6}Vert partial _xtheta ^{(0)}Vert _{H^b}lesssim nu ^{1/3})</span>, where <span>(bge 2)</span>.</p></div>","PeriodicalId":649,"journal":{"name":"Journal of Mathematical Fluid Mechanics","volume":"27 4","pages":""},"PeriodicalIF":1.3,"publicationDate":"2025-10-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145352616","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
Long-time Confinement near Special Vortex Crystals 特殊涡旋晶体附近的长时间约束
IF 1.3 3区 数学
Journal of Mathematical Fluid Mechanics Pub Date : 2025-10-22 DOI: 10.1007/s00021-025-00979-3
Martin Donati
{"title":"Long-time Confinement near Special Vortex Crystals","authors":"Martin Donati","doi":"10.1007/s00021-025-00979-3","DOIUrl":"10.1007/s00021-025-00979-3","url":null,"abstract":"<div><p>In this paper, we control the growth of the support of particular solutions to the Euler two-dimensional equations, whose vorticity is concentrated near special vortex crystals. These vortex crystals belong to the classical family of regular polygons with a central vortex, where we choose a particular intensity for the central vortex to have strong stability properties. A special case is the regular pentagon with no central vortex which also satisfies the stability properties required for the long-time confinement to work.</p></div>","PeriodicalId":649,"journal":{"name":"Journal of Mathematical Fluid Mechanics","volume":"27 4","pages":""},"PeriodicalIF":1.3,"publicationDate":"2025-10-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145352558","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
Singular Weak Solutions Near Boundaries in a Half-space Away from Localized Force for the Stokes and Navier-Stokes Equations Stokes方程和Navier-Stokes方程的半空间离局域力边界附近的奇异弱解
IF 1.3 3区 数学
Journal of Mathematical Fluid Mechanics Pub Date : 2025-10-12 DOI: 10.1007/s00021-025-00976-6
Tongkeun Chang, Kyungkeun Kang
{"title":"Singular Weak Solutions Near Boundaries in a Half-space Away from Localized Force for the Stokes and Navier-Stokes Equations","authors":"Tongkeun Chang,&nbsp;Kyungkeun Kang","doi":"10.1007/s00021-025-00976-6","DOIUrl":"10.1007/s00021-025-00976-6","url":null,"abstract":"<div><p>We prove that there exists a weak solution of the Stokes system with a non-zero external force and no-slip boundary conditions in a half-space of dimension three or higher such that its normal derivatives are unbounded near the boundary. A localized, divergence-free singular force causes, via a non-local effect, singular behavior of normal derivatives of the solution near the boundary, although this boundary is away from the support of the external force. The constructed solution is a weak solution with finite global energy, and it (can be compared to the one in Seregin and S̆verák (Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov. (POMI) 385 (2010), Kraevye Zadachi Matematicheskoĭ Fiziki i Smezhnye Voprosy Teorii Funktsiĭ. 41, 200–205, 236; J. Math. Sci. <b>178</b>, no. 3, 353–356 (2011)), which is a form of shear flow with only locally finite energy. A similar construction is performed) for the Navier-Stokes equations as well.</p></div>","PeriodicalId":649,"journal":{"name":"Journal of Mathematical Fluid Mechanics","volume":"27 4","pages":""},"PeriodicalIF":1.3,"publicationDate":"2025-10-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145316082","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
On the Modeling of Nonlinear Wind-Induced Ice-Drift Ocean Currents at the North Pole 北极非线性风致冰漂洋流的模拟研究
IF 1.3 3区 数学
Journal of Mathematical Fluid Mechanics Pub Date : 2025-10-03 DOI: 10.1007/s00021-025-00975-7
Christian Puntini
{"title":"On the Modeling of Nonlinear Wind-Induced Ice-Drift Ocean Currents at the North Pole","authors":"Christian Puntini","doi":"10.1007/s00021-025-00975-7","DOIUrl":"10.1007/s00021-025-00975-7","url":null,"abstract":"<div><p>Starting from the governing equations for geophysical flows, by means of a thin-shell approximation and a tangent plane approximation, we derive the equations describing, at leading order, the nonlinear ice-drift flow for regions centered around the North Pole. An exact solution is derived in the material/Lagrangian formalism, describing a superposition of oscillations, a mean Ekman flow, and a geostrophic current.</p></div>","PeriodicalId":649,"journal":{"name":"Journal of Mathematical Fluid Mechanics","volume":"27 4","pages":""},"PeriodicalIF":1.3,"publicationDate":"2025-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00021-025-00975-7.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145210239","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
Global Existence of a Quasi-Linear Hyperbolic-Parabolic Model for Vasculogenesis 血管生成的拟线性双曲-抛物模型的整体存在性
IF 1.3 3区 数学
Journal of Mathematical Fluid Mechanics Pub Date : 2025-10-03 DOI: 10.1007/s00021-025-00974-8
Qing Chen, Yunshun Wu
{"title":"Global Existence of a Quasi-Linear Hyperbolic-Parabolic Model for Vasculogenesis","authors":"Qing Chen,&nbsp;Yunshun Wu","doi":"10.1007/s00021-025-00974-8","DOIUrl":"10.1007/s00021-025-00974-8","url":null,"abstract":"<div><p>In this paper, we study the global existence for a quasi-linear hyperbolic-parabolic system modeling vascular networks. Under the assumption that the critical cell density satisfies <span>(P'(bar{rho })=frac{amu }{b}bar{rho })</span>, we establish the global existence for small perturbations and derive the optimal convergent rates for all-order derivatives of the solution.</p></div>","PeriodicalId":649,"journal":{"name":"Journal of Mathematical Fluid Mechanics","volume":"27 4","pages":""},"PeriodicalIF":1.3,"publicationDate":"2025-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145210251","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
Variational Derivation of the Geophysical Green-Naghdi Shallow-water System 地球物理Green-Naghdi浅水系统的变分推导
IF 1.3 3区 数学
Journal of Mathematical Fluid Mechanics Pub Date : 2025-09-11 DOI: 10.1007/s00021-025-00973-9
Yue Chen, Xingxing Liu
{"title":"Variational Derivation of the Geophysical Green-Naghdi Shallow-water System","authors":"Yue Chen,&nbsp;Xingxing Liu","doi":"10.1007/s00021-025-00973-9","DOIUrl":"10.1007/s00021-025-00973-9","url":null,"abstract":"<div><p>Under the shallow-water regime and without assuming wave amplitude smallness, we apply the variational approach in the Lagrangian formalism to derive the geophysical Green-Naghdi system. In contrast to the prior derivation in (Fan et al., J. Nonlinear Sci., <b>32</b>(21), 30 (2022)) that imposed a columnar-flow Ansatz, our method adopts the irrotational-flow assumption (which Fan et al., J. Nonlinear Sci., <b>32</b>(21), 30 (2022) does not), thereby generating the depth-independent horizontal velocity at leading order.</p></div>","PeriodicalId":649,"journal":{"name":"Journal of Mathematical Fluid Mechanics","volume":"27 4","pages":""},"PeriodicalIF":1.3,"publicationDate":"2025-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145037502","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
Global Existence and Vanishing Dispersion Limit of Strong/Classical Solutions to the One-dimensional Compressible Quantum Navier-Stokes Equations with Large Initial Data 具有大初始数据的一维可压缩量子Navier-Stokes方程强/经典解的整体存在性和消失色散极限
IF 1.3 3区 数学
Journal of Mathematical Fluid Mechanics Pub Date : 2025-09-09 DOI: 10.1007/s00021-025-00966-8
Zhengzheng Chen, Huijiang Zhao
{"title":"Global Existence and Vanishing Dispersion Limit of Strong/Classical Solutions to the One-dimensional Compressible Quantum Navier-Stokes Equations with Large Initial Data","authors":"Zhengzheng Chen,&nbsp;Huijiang Zhao","doi":"10.1007/s00021-025-00966-8","DOIUrl":"10.1007/s00021-025-00966-8","url":null,"abstract":"<div><p>We are concerned with the global existence and vanishing dispersion limit of strong/classical solutions to the Cauchy problem of the one-dimensional isentropic compressible quantum Navier-Stokes equations, which consists of the compressible Navier-Stokes equations with a linearly density-dependent viscosity and a nonlinear third-order differential operator known as the quantum Bohm potential. The pressure <span>(p(rho )=rho ^gamma )</span> is considered with <span>(gamma ge 1)</span> being a constant. We focus on the case when the Planck constant <span>(varepsilon )</span> and the viscosity constant <span>(nu )</span> are not equal. Under some suitable assumptions on <span>(varepsilon , nu , gamma )</span>, and the initial data, we proved the global existence and large-time behavior of strong and classical solutions away from vacuum to the compressible quantum Navier-Stokes equations with arbitrarily large initial data. This result extends the previous ones on the construction of global strong large-amplitude solutions of the compressible quantum Navier-Stokes equations to the case <span>(varepsilon ne nu )</span>. Moreover, the vanishing dispersion limit for the classical solutions of the quantum Navier-Stokes equations is also established with certain convergence rates. The proof is based on a new effective velocity which converts the quantum Navier-Stokes equations into a parabolic system, and some elaborate estimates to derive the uniform-in-time positive lower and upper bounds on the specific volume.</p></div>","PeriodicalId":649,"journal":{"name":"Journal of Mathematical Fluid Mechanics","volume":"27 4","pages":""},"PeriodicalIF":1.3,"publicationDate":"2025-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145021719","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
Dynamical Stability of Transonic Shock Solutions to Euler-Poisson System in an Annulus 环空中欧拉-泊松系统跨音速激波解的动力稳定性
IF 1.3 3区 数学
Journal of Mathematical Fluid Mechanics Pub Date : 2025-09-05 DOI: 10.1007/s00021-025-00961-z
Qifeng Bai, Yuanyuan Xing
{"title":"Dynamical Stability of Transonic Shock Solutions to Euler-Poisson System in an Annulus","authors":"Qifeng Bai,&nbsp;Yuanyuan Xing","doi":"10.1007/s00021-025-00961-z","DOIUrl":"10.1007/s00021-025-00961-z","url":null,"abstract":"<div><p>This paper concerns the Euler-Poisson system in an annulus with finite radius. The dynamical stability of radially symmetric transonic shock solutions to the Euler-Poisson system is transformed into the global well-posedness of a free boundary problem for a second-order quasilinear hyperbolic equation. One of the crucial ingredients of the analysis is to establish an energy estimate for the associated initial boundary value problem. The steady radial transonic shock solutions are proved to be dynamically and exponentially stable with respect to small perturbations of the initial data.</p></div>","PeriodicalId":649,"journal":{"name":"Journal of Mathematical Fluid Mechanics","volume":"27 4","pages":""},"PeriodicalIF":1.3,"publicationDate":"2025-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144990456","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
Steady Compressible Navier-Stokes-Fourier System with Slip Boundary Conditions Arising from Kinetic Theory 具有滑移边界条件的稳定可压缩Navier-Stokes-Fourier系统
IF 1.3 3区 数学
Journal of Mathematical Fluid Mechanics Pub Date : 2025-09-03 DOI: 10.1007/s00021-025-00972-w
Renjun Duan, Junhao Zhang
{"title":"Steady Compressible Navier-Stokes-Fourier System with Slip Boundary Conditions Arising from Kinetic Theory","authors":"Renjun Duan,&nbsp;Junhao Zhang","doi":"10.1007/s00021-025-00972-w","DOIUrl":"10.1007/s00021-025-00972-w","url":null,"abstract":"<div><p>This paper studies the boundary value problem on the steady compressible Navier-Stokes-Fourier system in a channel domain <span>((0,1)times mathbb {T}^2)</span> with a class of generalized slip boundary conditions that were systematically derived from the Boltzmann equation by Coron [9] and later by Aoki et al [1]. We establish the existence and uniqueness of strong solutions in <span>((L_{0}^{2}cap H^{2}(Omega ))times V^{3}(Omega )times H^{3}(Omega ))</span> provided that the wall temperature is near a positive constant. The proof relies on the construction of a new variational formulation for the corresponding linearized problem and employs a fixed point argument. The main difficulty arises from the interplay of velocity and temperature derivatives together with the effect of density dependence on the boundary.</p></div>","PeriodicalId":649,"journal":{"name":"Journal of Mathematical Fluid Mechanics","volume":"27 4","pages":""},"PeriodicalIF":1.3,"publicationDate":"2025-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144929355","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
Energy Equality for the Compressible Primitive Equations with Vacuum 带真空的可压缩原始方程的能量等式
IF 1.3 3区 数学
Journal of Mathematical Fluid Mechanics Pub Date : 2025-08-25 DOI: 10.1007/s00021-025-00970-y
šárka Nečasová, María Ángeles Rodríguez-Bellido, Tong Tang
{"title":"Energy Equality for the Compressible Primitive Equations with Vacuum","authors":"šárka Nečasová,&nbsp;María Ángeles Rodríguez-Bellido,&nbsp;Tong Tang","doi":"10.1007/s00021-025-00970-y","DOIUrl":"10.1007/s00021-025-00970-y","url":null,"abstract":"<div><p>The paper deals with the problem of the energy conservation for the weak solutions to the compressible Primitive Equations (CPE) system with degenerate viscosity. The sufficient conditions on the regularity of weak solutions for the energy equality are obtained even for the case when the solutions may include vacuum. In this paper, we show two theorems, the first one gives regularity in the classical isotropic Sobolev and Besov spaces. The second one states regularity in the anisotropic spaces. We obtain new regularity results in the second theorem due to the special structure of CPE system, which are in contrast to compressible Navier-Stokes equations.</p></div>","PeriodicalId":649,"journal":{"name":"Journal of Mathematical Fluid Mechanics","volume":"27 4","pages":""},"PeriodicalIF":1.3,"publicationDate":"2025-08-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144893926","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
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