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On the Effect of a Large Cloud of Rigid Particles on the Motion of an Incompressible Non–Newtonian Fluid 一大片刚性粒子云对不可压缩非牛顿流体运动的影响
IF 1.2 3区 数学
Journal of Mathematical Fluid Mechanics Pub Date : 2025-05-25 DOI: 10.1007/s00021-025-00944-0
Eduard Feireisl, Arnab Roy, Arghir Zarnescu
{"title":"On the Effect of a Large Cloud of Rigid Particles on the Motion of an Incompressible Non–Newtonian Fluid","authors":"Eduard Feireisl,&nbsp;Arnab Roy,&nbsp;Arghir Zarnescu","doi":"10.1007/s00021-025-00944-0","DOIUrl":"10.1007/s00021-025-00944-0","url":null,"abstract":"<div><p>We show that the collective effect of <i>N</i> rigid bodies <span>((mathcal {S}_{n,N})_{n=1}^N)</span> of diameters <span>((r_{n,N})_{n=1}^N)</span> immersed in an incompressible non–Newtonian fluid is negligible in the asymptotic limit <span>(N rightarrow infty )</span> as long as their total packing volume <span>(sum _{n=1}^N r_{n,N}^d)</span>, <span>(d=2,3)</span> tends to zero exponentially – <span>({sum _{n=1}^N r_{n,N}^d approx A^{-N}})</span> – for a certain constant <span>(A &gt; 1)</span>. The result is rather surprising and in a sharp contrast with the associated homogenization problem, where the same number of obstacles can completely stop the fluid motion in the case of shear thickening viscosity. A large class of non–Newtonian fluids is included, for which the viscous stress is a subdifferential of a convex potential.</p></div>","PeriodicalId":649,"journal":{"name":"Journal of Mathematical Fluid Mechanics","volume":"27 3","pages":""},"PeriodicalIF":1.2,"publicationDate":"2025-05-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00021-025-00944-0.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144131471","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
Strong Convergence of Low Mach Number Limit for the Compressible Navier–Stokes Equations in the Scaling Critical Spaces 尺度临界空间中可压缩Navier-Stokes方程低马赫数极限的强收敛性
IF 1.2 3区 数学
Journal of Mathematical Fluid Mechanics Pub Date : 2025-05-24 DOI: 10.1007/s00021-025-00938-y
Shozo Ogino
{"title":"Strong Convergence of Low Mach Number Limit for the Compressible Navier–Stokes Equations in the Scaling Critical Spaces","authors":"Shozo Ogino","doi":"10.1007/s00021-025-00938-y","DOIUrl":"10.1007/s00021-025-00938-y","url":null,"abstract":"<div><p>We consider the Cauchy problem for the compressible Navier–Stokes equations in whole space and low Mach number limit problem. In this paper, we show that the incompressible part of the velocity strongly converges to the solution of the incompressible Navier–Stokes equations as the Mach number goes to 0 in the scaling critical space. We also show that the density and the compressible part of the velocity vanish. Moreover, we derive the diverging of the time derivative of the compressible part of the velocity as Mach number goes to 0. The proofs are based on the <span>(L^1)</span>-Maximal regularity for the heat equations and the Strichartz estimates for the wave equations.</p></div>","PeriodicalId":649,"journal":{"name":"Journal of Mathematical Fluid Mechanics","volume":"27 3","pages":""},"PeriodicalIF":1.2,"publicationDate":"2025-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00021-025-00938-y.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144131473","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
Temperature Dependent Precipitation in Exact Nonlinear Mountain Waves 精确非线性山波中的温度相关降水
IF 1.2 3区 数学
Journal of Mathematical Fluid Mechanics Pub Date : 2025-05-24 DOI: 10.1007/s00021-025-00946-y
Tony Lyons, Jordan McCarney
{"title":"Temperature Dependent Precipitation in Exact Nonlinear Mountain Waves","authors":"Tony Lyons,&nbsp;Jordan McCarney","doi":"10.1007/s00021-025-00946-y","DOIUrl":"10.1007/s00021-025-00946-y","url":null,"abstract":"<div><p>Lagrangian variables are used to develop an explicit description of nonlinear mountain waves propagating in a moist atmosphere. This Lagrangian description is used to deduce an integral representation of the atmospheric pressure distribution in terms of the temperature within the laminar flow layer. Kirchoff’s equation is used to determine a temperature dependent enthalpy which together with the Clausius-Clapeyron equation is used to obtain an explicit expression for temperature and vapour pressure profiles in a saturated atmosphere where mountain waves are prominent. Precipitation rates are computed from the first law of thermodynamics and compare favourably with meteorological field data at Feldberg, a mountain in Germany. The second law of thermodynamics is used to show that there is a subregion near the tropopause at which precipitation is prohibited within the laminar flow.</p></div>","PeriodicalId":649,"journal":{"name":"Journal of Mathematical Fluid Mechanics","volume":"27 3","pages":""},"PeriodicalIF":1.2,"publicationDate":"2025-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00021-025-00946-y.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144131472","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
Spectral Stability of Multi-Solitons for the Kaup-Kupershmidt Equation kup - kupershmidt方程多孤子的谱稳定性
IF 1.2 3区 数学
Journal of Mathematical Fluid Mechanics Pub Date : 2025-05-14 DOI: 10.1007/s00021-025-00942-2
Zhong Wang
{"title":"Spectral Stability of Multi-Solitons for the Kaup-Kupershmidt Equation","authors":"Zhong Wang","doi":"10.1007/s00021-025-00942-2","DOIUrl":"10.1007/s00021-025-00942-2","url":null,"abstract":"<div><p>Spectral stability analysis of ”anomalous” solitons and multi-solitons is presented in the context of a generalized Hamiltonian system called the Kaup-Kupershmidt (KK) equation. The KK equation is a completely integrable fifth order Korteweg-de Vries equation, which admits third order eigenvalue problem in its Lax pair. We also prove Hamiltonian-Krein index identities in verifying stability criterion of its multi-solitons. However, the KK equation does not possess the <span>(L^2)</span> conservation law and the linearized operators around the multi-solitons have no spectral gap. The main ingredients of the proof are new operator identities for second variation operator and completeness in <span>(L^2)</span> of the squared eigenfunctions of the third order eigenvalue problem for the KK equation. The operator identities and completeness relation are shown by employing the recursion operators of the KK equation.</p></div>","PeriodicalId":649,"journal":{"name":"Journal of Mathematical Fluid Mechanics","volume":"27 3","pages":""},"PeriodicalIF":1.2,"publicationDate":"2025-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143949568","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 Pathwise Uniqueness of Stochastic 2D Euler Equations with Kraichnan Noise and (L^p)-data 具有Kraichnan噪声和(L^p) -数据的随机二维欧拉方程的路径唯一性
IF 1.2 3区 数学
Journal of Mathematical Fluid Mechanics Pub Date : 2025-05-14 DOI: 10.1007/s00021-025-00943-1
Shuaijie Jiao, Dejun Luo
{"title":"On the Pathwise Uniqueness of Stochastic 2D Euler Equations with Kraichnan Noise and (L^p)-data","authors":"Shuaijie Jiao,&nbsp;Dejun Luo","doi":"10.1007/s00021-025-00943-1","DOIUrl":"10.1007/s00021-025-00943-1","url":null,"abstract":"<div><p>In the recent work [arXiv:2308.03216], Coghi and Maurelli proved pathwise uniqueness of solutions to the vorticity form of stochastic 2D Euler equation, with Kraichnan transport noise and initial data in <span>(L^1cap L^p)</span> for <span>(p&gt;3/2)</span>. The aim of this note is to remove the constraint on <i>p</i>, showing that pathwise uniqueness holds for all <span>(L^1cap L^p)</span> initial data with arbitrary <span>(p&gt;1)</span>.</p></div>","PeriodicalId":649,"journal":{"name":"Journal of Mathematical Fluid Mechanics","volume":"27 3","pages":""},"PeriodicalIF":1.2,"publicationDate":"2025-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143949651","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 Basic Velocity Estimates for the Plane Steady-State Navier–Stokes System and Its Applications 平面稳态Navier-Stokes系统的基本速度估计及其应用
IF 1.2 3区 数学
Journal of Mathematical Fluid Mechanics Pub Date : 2025-05-10 DOI: 10.1007/s00021-025-00939-x
Mikhail Korobkov, Xiao Ren
{"title":"On Basic Velocity Estimates for the Plane Steady-State Navier–Stokes System and Its Applications","authors":"Mikhail Korobkov,&nbsp;Xiao Ren","doi":"10.1007/s00021-025-00939-x","DOIUrl":"10.1007/s00021-025-00939-x","url":null,"abstract":"<div><p>We consider some new estimates for general steady Navier–Stokes solutions in plane domains. According to our main result, if the domain is convex, then the difference between mean values of the velocity over two concentric circles is bounded (up to a constant factor) by the square-root of the Dirichlet integral in the annulus between the circles. The constant factor in this inequality is universal and does not depend on the ratio of the circle radii. Several applications of these formulas are discussed.</p></div>","PeriodicalId":649,"journal":{"name":"Journal of Mathematical Fluid Mechanics","volume":"27 3","pages":""},"PeriodicalIF":1.2,"publicationDate":"2025-05-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143930112","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 a Two-Component Shallow-Water Model with the Weak Coriolis and Equatorial Undercurrent Effects 具有弱科里奥利效应和赤道潜流效应的双分量浅水模式
IF 1.2 3区 数学
Journal of Mathematical Fluid Mechanics Pub Date : 2025-05-09 DOI: 10.1007/s00021-025-00940-4
Lili Huang, Yaojun Yang, Shouming Zhou
{"title":"On a Two-Component Shallow-Water Model with the Weak Coriolis and Equatorial Undercurrent Effects","authors":"Lili Huang,&nbsp;Yaojun Yang,&nbsp;Shouming Zhou","doi":"10.1007/s00021-025-00940-4","DOIUrl":"10.1007/s00021-025-00940-4","url":null,"abstract":"<div><p>The present paper studies a two-component mathematical model representing shallow-water wave propagation primarily in equatorial ocean regions, incorporating the effects of weak Coriolis force and equatorial undercurrent. We start with the Green–Naghdi type equations under the weak Coriolis and equatorial undercurrent effects from the Euler equations, then the two-component Camassa–Holm system with the two effects is derived by truncating asymptotic expansions of the quantities to the appropriate order. Analytically, we study the mathematical properties of the solutions to the two-component Camassa–Holm system including the ill-posedness of the solutions in Besov spaces <span>(B^{s}_{p,infty }times B^{s-1}_{p,infty })</span> with <span>(1le ple infty )</span> and <span>(s&gt;max left{ 2+frac{1}{p},frac{5}{2}right} )</span>, the Hölder continuity of the data-to-solution map in Besov spaces <span>(B^{s}_{p,r}times B^{s-1}_{p,r})</span> with <span>(1le p,rle infty )</span> and <span>(s&gt;max left{ 2+frac{1}{p},frac{5}{2}right} )</span>. We then investigate the Gevrey regularity and analyticity of the system in <span>({G_{delta ,s}^{gamma }}times {G_{delta ,s-1}^{gamma }})</span> with <span>(delta ge 1, nu&gt;gamma &gt;0)</span> and <span>(s&gt;frac{5}{2})</span>. Finally, we provide the persistence properties and the spatial asymptotic profiles of the solutions in weighted spaces <span>(L ^ p_{phi }=L^p(mathbb {R},phi ^pdx))</span>.</p></div>","PeriodicalId":649,"journal":{"name":"Journal of Mathematical Fluid Mechanics","volume":"27 3","pages":""},"PeriodicalIF":1.2,"publicationDate":"2025-05-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143925679","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
Saint-Venant Estimates and Liouville-Type Theorems for the Stationary Navier–Stokes Equation in (mathbb {R}^3) 中平稳Navier-Stokes方程的Saint-Venant估计和liouville型定理 (mathbb {R}^3)
IF 1.2 3区 数学
Journal of Mathematical Fluid Mechanics Pub Date : 2025-05-08 DOI: 10.1007/s00021-025-00941-3
Jeaheang Bang, Zhuolun Yang
{"title":"Saint-Venant Estimates and Liouville-Type Theorems for the Stationary Navier–Stokes Equation in (mathbb {R}^3)","authors":"Jeaheang Bang,&nbsp;Zhuolun Yang","doi":"10.1007/s00021-025-00941-3","DOIUrl":"10.1007/s00021-025-00941-3","url":null,"abstract":"<div><p>We prove two Liouville-type theorems for the stationary Navier–Stokes equations in <span>(mathbb {R}^3)</span> under some assumptions on 1) the growth of the <span>(L^s)</span> mean oscillation of a potential function of the velocity field, or 2) the relative decay of the head pressure and the square of the velocity field at infinity. The main idea is to use Saint-Venant type estimates to characterize the growth of Dirichlet energy of nontrivial solutions. These assumptions are weaker than those previously known of a similar nature.</p></div>","PeriodicalId":649,"journal":{"name":"Journal of Mathematical Fluid Mechanics","volume":"27 3","pages":""},"PeriodicalIF":1.2,"publicationDate":"2025-05-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143925698","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
A Simple Proof of Linear Instability of Shear Flows with Application to Vortex Sheets 切变流线性不稳定性的简单证明及其在涡片上的应用
IF 1.2 3区 数学
Journal of Mathematical Fluid Mechanics Pub Date : 2025-05-05 DOI: 10.1007/s00021-025-00937-z
Anuj Kumar, Wojciech Ożański
{"title":"A Simple Proof of Linear Instability of Shear Flows with Application to Vortex Sheets","authors":"Anuj Kumar,&nbsp;Wojciech Ożański","doi":"10.1007/s00021-025-00937-z","DOIUrl":"10.1007/s00021-025-00937-z","url":null,"abstract":"<div><p>We consider the construction of linear instability of parallel shear flows, which was developed by Lin (SIAM J Math Anal 35(2):318–356, 2003). We give an alternative simple proof in Sobolev setting of the problem, which exposes the mathematical role of the Plemelj–Sochocki formula in the emergence of the instability, as well as does not require the cone condition. Moreover, we localize this approach to obtain an approximation of the Kelvin–Helmholtz instability of a flat vortex sheet.\u0000</p></div>","PeriodicalId":649,"journal":{"name":"Journal of Mathematical Fluid Mechanics","volume":"27 3","pages":""},"PeriodicalIF":1.2,"publicationDate":"2025-05-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143904860","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
Construction of Low Regularity Strong Solutions to the Viscous Surface Wave Equations 粘性表面波方程低正则性强解的构造
IF 1.2 3区 数学
Journal of Mathematical Fluid Mechanics Pub Date : 2025-04-23 DOI: 10.1007/s00021-025-00936-0
Guilong Gui, Yancan Li
{"title":"Construction of Low Regularity Strong Solutions to the Viscous Surface Wave Equations","authors":"Guilong Gui,&nbsp;Yancan Li","doi":"10.1007/s00021-025-00936-0","DOIUrl":"10.1007/s00021-025-00936-0","url":null,"abstract":"<div><p>We construct in the paper the low-regularity strong solutions to the viscous surface wave equations in anisotropic Sobolev spaces. By using the Lagrangian structure of the system to homogenize the free boundary conditions coupled with the semigroup method of the linear operator, we establish a new iteration scheme on a known equilibrium domain to get the low-regularity strong solutions, in which no compatibility conditions of the accelerated velocity on the initial data are required.\u0000</p></div>","PeriodicalId":649,"journal":{"name":"Journal of Mathematical Fluid Mechanics","volume":"27 2","pages":""},"PeriodicalIF":1.2,"publicationDate":"2025-04-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143865512","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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