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Optimality of the Decay Estimate of Solutions to the Linearised Curl-Free Compressible Navier–Stokes Equations 线性化无旋流可压缩Navier-Stokes方程解衰减估计的最优性
IF 1.3 3区 数学
Journal of Mathematical Fluid Mechanics Pub Date : 2023-11-14 DOI: 10.1007/s00021-023-00837-0
Tsukasa Iwabuchi, Dáithí Ó hAodha
{"title":"Optimality of the Decay Estimate of Solutions to the Linearised Curl-Free Compressible Navier–Stokes Equations","authors":"Tsukasa Iwabuchi,&nbsp;Dáithí Ó hAodha","doi":"10.1007/s00021-023-00837-0","DOIUrl":"10.1007/s00021-023-00837-0","url":null,"abstract":"<div><p>We discuss optimal estimates of solutions to the compressible Navier–Stokes equations in Besov norms. In particular, we consider the estimate of the curl-free part of the solution to the linearised equations, in the homogeneous case. We prove that our estimate is optimal in the <span>(L^infty )</span>-norm by showing that the norm is bounded from below by the same decay rate.\u0000</p></div>","PeriodicalId":649,"journal":{"name":"Journal of Mathematical Fluid Mechanics","volume":"26 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2023-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00021-023-00837-0.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134878289","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: 2
A Method for Finding Exact Solutions to the 2D and 3D Euler–Boussinesq Equations in Lagrangian Coordinates 拉格朗日坐标系下二维和三维Euler-Boussinesq方程精确解的一种方法
IF 1.3 3区 数学
Journal of Mathematical Fluid Mechanics Pub Date : 2023-11-14 DOI: 10.1007/s00021-023-00835-2
Tomi Saleva, Jukka Tuomela
{"title":"A Method for Finding Exact Solutions to the 2D and 3D Euler–Boussinesq Equations in Lagrangian Coordinates","authors":"Tomi Saleva,&nbsp;Jukka Tuomela","doi":"10.1007/s00021-023-00835-2","DOIUrl":"10.1007/s00021-023-00835-2","url":null,"abstract":"<div><p>We study the Boussinesq approximation for the incompressible Euler equations using Lagrangian description. The conditions for the Lagrangian fluid map are derived in this setting, and a general method is presented to find exact fluid flows in both the two-dimensional and the three-dimensional case. There is a vast amount of solutions obtainable with this method and we can only showcase a handful of interesting examples here, including a Gerstner type solution to the two-dimensional Euler–Boussinesq equations. In two earlier papers we used the same method to find exact Lagrangian solutions to the homogeneous Euler equations, and this paper serves as an example of how these same ideas can be extended to provide solutions also to related, more involved models.</p></div>","PeriodicalId":649,"journal":{"name":"Journal of Mathematical Fluid Mechanics","volume":"26 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2023-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00021-023-00835-2.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134796342","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
Nearly Toroidal, Periodic and Quasi-periodic Motions of Fluid Particles Driven by the Gavrilov Solutions of the Euler Equations Euler方程Gavrilov解驱动下流体粒子的近环面、周期和准周期运动
IF 1.3 3区 数学
Journal of Mathematical Fluid Mechanics Pub Date : 2023-11-07 DOI: 10.1007/s00021-023-00836-1
Pietro Baldi
{"title":"Nearly Toroidal, Periodic and Quasi-periodic Motions of Fluid Particles Driven by the Gavrilov Solutions of the Euler Equations","authors":"Pietro Baldi","doi":"10.1007/s00021-023-00836-1","DOIUrl":"10.1007/s00021-023-00836-1","url":null,"abstract":"<div><p>We consider the smooth, compactly supported solutions of the steady 3D Euler equations of incompressible fluids constructed by Gavrilov (Geom Funct Anal (GAFA) 29(1):190–197, 2019), and we study the corresponding fluid particle dynamics. This is an <span>ode</span> analysis, which contributes to the description of Gavrilov’s vector field.</p></div>","PeriodicalId":649,"journal":{"name":"Journal of Mathematical Fluid Mechanics","volume":"26 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2023-11-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00021-023-00836-1.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71909781","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: 1
Allen–Cahn–Navier–Stokes–Voigt Systems with Moving Contact Lines 具有移动接触线的Allen-Cahn-Navier-Stokes-Voigt系统
IF 1.3 3区 数学
Journal of Mathematical Fluid Mechanics Pub Date : 2023-10-31 DOI: 10.1007/s00021-023-00829-0
Ciprian G. Gal, Maurizio Grasselli, Andrea Poiatti
{"title":"Allen–Cahn–Navier–Stokes–Voigt Systems with Moving Contact Lines","authors":"Ciprian G. Gal,&nbsp;Maurizio Grasselli,&nbsp;Andrea Poiatti","doi":"10.1007/s00021-023-00829-0","DOIUrl":"10.1007/s00021-023-00829-0","url":null,"abstract":"<div><p>We consider a diffuse interface model for an incompressible binary fluid flow. The model consists of the Navier–Stokes–Voigt equations coupled with the mass-conserving Allen–Cahn equation with Flory–Huggins potential. The resulting system is subject to generalized Navier boundary conditions for the (volume averaged) fluid velocity <span>({{textbf {u}}})</span> and to a dynamic contact line boundary condition for the order parameter <span>(phi )</span>. These boundary conditions account for the moving contact line phenomenon. We establish the existence of a global weak solution which satisfies an energy inequality. A similar result is proven for the Allen–Cahn–Navier–Stokes system. In order to obtain some higher-order regularity (w.r.t. time) we propose the Voigt approximation: in this way we are able to prove the validity of the energy identity and of the strict separation property. Thanks to this property, we can show the uniqueness of quasi-strong solutions, even in dimension three. Regularization in finite time of weak solutions is also shown.</p></div>","PeriodicalId":649,"journal":{"name":"Journal of Mathematical Fluid Mechanics","volume":"25 4","pages":""},"PeriodicalIF":1.3,"publicationDate":"2023-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134797829","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: 3
The Lagrangian Formulation for Wave Motion with a Shear Current and Surface Tension 具有剪切流和表面张力的波动的拉格朗日公式
IF 1.3 3区 数学
Journal of Mathematical Fluid Mechanics Pub Date : 2023-10-17 DOI: 10.1007/s00021-023-00831-6
Conor Curtin, Rossen Ivanov
{"title":"The Lagrangian Formulation for Wave Motion with a Shear Current and Surface Tension","authors":"Conor Curtin,&nbsp;Rossen Ivanov","doi":"10.1007/s00021-023-00831-6","DOIUrl":"10.1007/s00021-023-00831-6","url":null,"abstract":"<div><p>The Lagrangian formulation for the irrotational wave motion is straightforward and follows from a Lagrangian functional which is the difference between the kinetic and the potential energy of the system. In the case of fluid with constant vorticity, which arises for example when a shear current is present, the separation of the energy into kinetic and potential is not at all obvious and neither is the Lagrangian formulation of the problem. Nevertheless, we use the known Hamiltonian formulation of the problem in this case to obtain the Lagrangian density function, and utilising the Euler–Lagrange equations we proceed to derive some model equations for different propagation regimes. While the long-wave regime reproduces the well known KdV equation, the short- and intermediate long wave regimes lead to highly nonlinear and nonlocal evolution equations.</p></div>","PeriodicalId":649,"journal":{"name":"Journal of Mathematical Fluid Mechanics","volume":"25 4","pages":""},"PeriodicalIF":1.3,"publicationDate":"2023-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134796671","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
Regularity Criterion for the 2D Inviscid Boussinesq Equations 二维无粘Boussinesq方程的正则性判据
IF 1.3 3区 数学
Journal of Mathematical Fluid Mechanics Pub Date : 2023-10-17 DOI: 10.1007/s00021-023-00832-5
Menghan Gong, Zhuan Ye
{"title":"Regularity Criterion for the 2D Inviscid Boussinesq Equations","authors":"Menghan Gong,&nbsp;Zhuan Ye","doi":"10.1007/s00021-023-00832-5","DOIUrl":"10.1007/s00021-023-00832-5","url":null,"abstract":"<div><p>The question of whether the two-dimensional inviscid Boussinesq equations can develop a finite-time singularity from general initial data is a challenging open problem. In this paper, we obtain two new regularity criteria for the local-in-time smooth solution to the two-dimensional inviscid Boussinesq equations. Similar result is also valid for the nonlocal perturbation of the two-dimensional incompressible Euler equations.</p></div>","PeriodicalId":649,"journal":{"name":"Journal of Mathematical Fluid Mechanics","volume":"25 4","pages":""},"PeriodicalIF":1.3,"publicationDate":"2023-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134796675","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 Stability and Decay for the 2D Incompressible Euler-Like Equations 二维不可压缩类欧拉方程的稳定性和衰减
IF 1.3 3区 数学
Journal of Mathematical Fluid Mechanics Pub Date : 2023-10-11 DOI: 10.1007/s00021-023-00824-5
Hongxia Lin, Qing Sun, Sen Liu, Heng Zhang
{"title":"The Stability and Decay for the 2D Incompressible Euler-Like Equations","authors":"Hongxia Lin,&nbsp;Qing Sun,&nbsp;Sen Liu,&nbsp;Heng Zhang","doi":"10.1007/s00021-023-00824-5","DOIUrl":"10.1007/s00021-023-00824-5","url":null,"abstract":"<div><p>This paper is concerned with the two-dimensional incompressible Euler-like equations. More precisely, we consider the system with only damping in the vertical component equation. When the domain is the whole space <span>(mathbb {R}^2)</span>, it is well known that solutions of the incompressible Euler equations can grow rapidly in time while solutions of the Euler equations with full damping are stable. As the intermediate case of the two equations, the global well-posedness and the stability in <span>(mathbb {R}^2)</span> remain the outstanding open problem. Our attentions here focus on the domain <span>(Omega =mathbb {T}times mathbb {R})</span> with <span>(mathbb {T})</span> being 1D periodic box. Compared with <span>(mathbb {R}^2)</span>, the domain <span>(Omega )</span> allows us to separate the physical quantity <i>f</i> into its horizontal average <span>(overline{f})</span> and the corresponding oscillation <span>(widetilde{f})</span>. By deriving the strong Poincaré inequality and two anisotropic inequalities related to <span>(widetilde{f})</span>, we are able to employ the time-weighted energy estimate to establish the stability of the solution and the precise large-time behavior of the system provided that the initial data is small and satisfies the reflection symmetry condition.</p></div>","PeriodicalId":649,"journal":{"name":"Journal of Mathematical Fluid Mechanics","volume":"25 4","pages":""},"PeriodicalIF":1.3,"publicationDate":"2023-10-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134796174","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
Fast Rotating Non-homogeneous Fluids in Thin Domains and the Ekman Pumping Effect 薄域中快速旋转非均匀流体与Ekman抽运效应
IF 1.3 3区 数学
Journal of Mathematical Fluid Mechanics Pub Date : 2023-10-03 DOI: 10.1007/s00021-023-00826-3
Marco Bravin, Francesco Fanelli
{"title":"Fast Rotating Non-homogeneous Fluids in Thin Domains and the Ekman Pumping Effect","authors":"Marco Bravin,&nbsp;Francesco Fanelli","doi":"10.1007/s00021-023-00826-3","DOIUrl":"10.1007/s00021-023-00826-3","url":null,"abstract":"<div><p>In this paper, we perform the fast rotation limit <span>(varepsilon rightarrow 0^+)</span> of the density-dependent incompressible Navier–Stokes–Coriolis system in a thin strip <span>(Omega _varepsilon :=,{mathbb {R}}^2times , left. right] -ell _varepsilon ,ell _varepsilon left[ right. ,)</span>, where <span>(varepsilon in ,left. right] 0,1left. right] )</span> is the size of the Rossby number and <span>(ell _varepsilon &gt;0)</span> for any <span>(varepsilon &gt;0)</span>. By letting <span>(ell _varepsilon longrightarrow 0^+)</span> for <span>(varepsilon rightarrow 0^+)</span> and considering Navier-slip boundary conditions at the boundary of <span>(Omega _varepsilon )</span>, we give a rigorous justification of the phenomenon of the Ekman pumping in the context of non-homogeneous fluids. With respect to previous studies (performed for flows of contant density and for compressible fluids), our approach has the advantage of circumventing the complicated analysis of boundary layers. To the best of our knowledge, this is the first study dealing with the asymptotic analysis of fast rotating incompressible fluids with variable density in a 3-D setting. In this respect, we remark that the case <span>(ell _varepsilon geqslant ell &gt;0)</span> for all <span>(varepsilon &gt;0)</span> remains largely open at present.</p></div>","PeriodicalId":649,"journal":{"name":"Journal of Mathematical Fluid Mechanics","volume":"25 4","pages":""},"PeriodicalIF":1.3,"publicationDate":"2023-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00021-023-00826-3.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134795369","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
Gevrey-Class-3 Regularity of the Linearised Hyperbolic Prandtl System on a Strip 条上线性化双曲Prandtl系统的gevrey -3类正则性
IF 1.3 3区 数学
Journal of Mathematical Fluid Mechanics Pub Date : 2023-09-01 DOI: 10.1007/s00021-023-00821-8
Francesco De Anna, Joshua Kortum, Stefano Scrobogna
{"title":"Gevrey-Class-3 Regularity of the Linearised Hyperbolic Prandtl System on a Strip","authors":"Francesco De Anna,&nbsp;Joshua Kortum,&nbsp;Stefano Scrobogna","doi":"10.1007/s00021-023-00821-8","DOIUrl":"10.1007/s00021-023-00821-8","url":null,"abstract":"<div><p>In the present paper, we address a physically-meaningful extension of the linearised Prandtl equations around a shear flow. Without any structural assumption, it is well-known that the optimal regularity of Prandtl is given by the class Gevrey 2 along the horizontal direction. The goal of this paper is to overcome this barrier, by dealing with the linearisation of the so-called <i>hyperbolic Prandtl equations</i> in a strip domain. We prove that the local well-posedness around a general shear flow <span>(U_{textrm{sh}}in W^{3, infty }(0,1))</span> holds true, with solutions that are Gevrey class 3 in the horizontal direction.</p></div>","PeriodicalId":649,"journal":{"name":"Journal of Mathematical Fluid Mechanics","volume":"25 4","pages":""},"PeriodicalIF":1.3,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00021-023-00821-8.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41487021","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: 2
The Optimal Temporal Decay Rates for Compressible Hall-magnetohydrodynamics System 可压缩霍尔-磁流体动力学系统的最佳时间衰减率
IF 1.3 3区 数学
Journal of Mathematical Fluid Mechanics Pub Date : 2023-08-26 DOI: 10.1007/s00021-023-00820-9
Shengbin Fu, Weiwei Wang
{"title":"The Optimal Temporal Decay Rates for Compressible Hall-magnetohydrodynamics System","authors":"Shengbin Fu,&nbsp;Weiwei Wang","doi":"10.1007/s00021-023-00820-9","DOIUrl":"10.1007/s00021-023-00820-9","url":null,"abstract":"<div><p>In this paper, we are interested in the global well-posedness of the strong solutions to the Cauchy problem on the compressible magnetohydrodynamics system with Hall effect. Moreover, we establish the convergence rates of the above solutions trending towards the constant equilibrium <span>(({bar{rho }},0,bar{textbf{B}}))</span>, provided that the initial perturbation belonging to <span>(H^3({mathbb {R}}^3) cap B_{2, infty }^{-s}({mathbb {R}}^3))</span> for <span>(s in (0,frac{3}{2}])</span> is sufficiently small.</p></div>","PeriodicalId":649,"journal":{"name":"Journal of Mathematical Fluid Mechanics","volume":"25 4","pages":""},"PeriodicalIF":1.3,"publicationDate":"2023-08-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4996997","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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