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Journal of Mathematical Fluid Mechanics最新文献

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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
Asymptotic Stability of Rarefaction Waves for Hyperbolized Compressible Navier–Stokes Equations 双曲可压缩Navier-Stokes方程稀疏波的渐近稳定性
IF 1.3 3区 数学
Journal of Mathematical Fluid Mechanics Pub Date : 2023-11-01 DOI: 10.1007/s00021-023-00833-4
Yuxi Hu, Xuefang Wang
{"title":"Asymptotic Stability of Rarefaction Waves for Hyperbolized Compressible Navier–Stokes Equations","authors":"Yuxi Hu,&nbsp;Xuefang Wang","doi":"10.1007/s00021-023-00833-4","DOIUrl":"10.1007/s00021-023-00833-4","url":null,"abstract":"<div><p>We consider a model of one dimensional isentropic compressible Navier–Stokes equations for which the classical Newtonian flow is replaced by a Maxwell flow. We establish the asymptotic stability of rarefaction waves for this model under some small conditions on initial perturbations and amplitude of the waves. The proof is based on <span>(L^2)</span> energy methods.\u0000</p></div>","PeriodicalId":649,"journal":{"name":"Journal of Mathematical Fluid Mechanics","volume":"25 4","pages":""},"PeriodicalIF":1.3,"publicationDate":"2023-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134795389","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
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
Global Existence of Strong Solutions and Serrin-Type Blowup Criterion for 3D Combustion Model in Bounded Domains 三维燃烧模型有界区域强解的整体存在性及serrin型爆破判据
IF 1.3 3区 数学
Journal of Mathematical Fluid Mechanics Pub Date : 2023-10-14 DOI: 10.1007/s00021-023-00830-7
Jiawen Zhang
{"title":"Global Existence of Strong Solutions and Serrin-Type Blowup Criterion for 3D Combustion Model in Bounded Domains","authors":"Jiawen Zhang","doi":"10.1007/s00021-023-00830-7","DOIUrl":"10.1007/s00021-023-00830-7","url":null,"abstract":"<div><p>The combustion model is studied in three-dimensional (3D) smooth bounded domains with various types of boundary conditions. The global existence and uniqueness of strong solutions are obtained under the smallness of the gradient of initial velocity in some precise sense. Using the energy method with the estimates of boundary integrals, we obtain the a priori bounds of the density and velocity field. Finally, we establish the blowup criterion for the 3D combustion system.</p></div>","PeriodicalId":649,"journal":{"name":"Journal of Mathematical Fluid Mechanics","volume":"25 4","pages":""},"PeriodicalIF":1.3,"publicationDate":"2023-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134796346","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
Mathematical Theory of Compressible Magnetohydrodynamics Driven by Non-conservative Boundary Conditions 非保守边界条件驱动下的可压缩磁流体力学数学理论
IF 1.3 3区 数学
Journal of Mathematical Fluid Mechanics Pub Date : 2023-10-07 DOI: 10.1007/s00021-023-00827-2
Eduard Feireisl, Piotr Gwiazda, Young-Sam Kwon, Agnieszka Świerczewska-Gwiazda
{"title":"Mathematical Theory of Compressible Magnetohydrodynamics Driven by Non-conservative Boundary Conditions","authors":"Eduard Feireisl,&nbsp;Piotr Gwiazda,&nbsp;Young-Sam Kwon,&nbsp;Agnieszka Świerczewska-Gwiazda","doi":"10.1007/s00021-023-00827-2","DOIUrl":"10.1007/s00021-023-00827-2","url":null,"abstract":"<div><p>We propose a new concept of weak solution to the equations of compressible magnetohydrodynamics driven by ihomogeneous boundary data. The system of the underlying field equations is solvable globally in time in the out of equilibrium regime characteristic for turbulence. The weak solutions comply with the weak–strong uniqueness principle; they coincide with the classical solution of the problem as long as the latter exists. The choice of constitutive relations is motivated by applications in stellar magnetoconvection.</p></div>","PeriodicalId":649,"journal":{"name":"Journal of Mathematical Fluid Mechanics","volume":"25 4","pages":""},"PeriodicalIF":1.3,"publicationDate":"2023-10-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00021-023-00827-2.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134795765","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
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
Symmetrization and Local Existence of Strong Solutions for Diffuse Interface Fluid Models 扩散界面流体模型强解的对称性与局部存在性
IF 1.3 3区 数学
Journal of Mathematical Fluid Mechanics Pub Date : 2023-09-28 DOI: 10.1007/s00021-023-00825-4
Vincent Giovangigli, Yoann Le Calvez, Flore Nabet
{"title":"Symmetrization and Local Existence of Strong Solutions for Diffuse Interface Fluid Models","authors":"Vincent Giovangigli,&nbsp;Yoann Le Calvez,&nbsp;Flore Nabet","doi":"10.1007/s00021-023-00825-4","DOIUrl":"10.1007/s00021-023-00825-4","url":null,"abstract":"<div><p>We investigate compressible nonisothermal diffuse interface fluid models also termed capillary fluids. Such fluid models involve van der Waals’ gradient energy, Korteweg’s tensor, Dunn and Serrin’s heat flux as well as diffusive fluxes. The density gradient is added as an extra variable and the convective and capillary fluxes of the augmented system are identified by using the Legendre transform of entropy. The augmented system of equations is recast into a normal form with symmetric hyperbolic first order terms, symmetric dissipative second order terms and antisymmetric capillary second order terms. New a priori estimates are obtained for such augmented system of equations in normal form. The time derivatives of the parabolic components are less regular than for standard hyperbolic–parabolic systems and the strongly coupling antisymmetric fluxes yields new majorizing terms. Using the augmented system in normal form and the a priori estimates, local existence of strong solutions is established in an Hilbertian framework.</p></div>","PeriodicalId":649,"journal":{"name":"Journal of Mathematical Fluid Mechanics","volume":"25 4","pages":""},"PeriodicalIF":1.3,"publicationDate":"2023-09-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134797926","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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