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Stability of Stationary Solutions to the Nonisentropic Euler–Poisson System in a Perturbed Half Space 摄动半空间中非等熵Euler-Poisson系统平稳解的稳定性
IF 1.3 3区 数学
Journal of Mathematical Fluid Mechanics Pub Date : 2025-08-25 DOI: 10.1007/s00021-025-00971-x
Mingjie Li, Masahiro Suzuki
{"title":"Stability of Stationary Solutions to the Nonisentropic Euler–Poisson System in a Perturbed Half Space","authors":"Mingjie Li,&nbsp;Masahiro Suzuki","doi":"10.1007/s00021-025-00971-x","DOIUrl":"10.1007/s00021-025-00971-x","url":null,"abstract":"<div><p>The main concern of this paper is to mathematically investigate the formation of a plasma sheath near the surface of nonplanar walls. We study the existence and asymptotic stability of stationary solutions for the nonisentropic Euler-Poisson equations in a domain of which boundary is drawn by a graph, by employing a space weighted energy method. Moreover, the convergence rate of the solution toward the stationary solution is obtained, provided that the initial perturbation belongs to the weighted Sobolev space. Because the domain is the perturbed half space, we first show the time-global solvability of the nonisentropic Euler-Poisson equations, then construct stationary solutions by using the time-global solutions.</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":"144893925","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
Supersonic Euler Flow Through a Two-dimensional Finite Straight Nozzle 二维有限直喷管中的超声速欧拉流
IF 1.3 3区 数学
Journal of Mathematical Fluid Mechanics Pub Date : 2025-08-23 DOI: 10.1007/s00021-025-00969-5
Qianfeng Li, Ting Xiao, Hairong Yuan
{"title":"Supersonic Euler Flow Through a Two-dimensional Finite Straight Nozzle","authors":"Qianfeng Li,&nbsp;Ting Xiao,&nbsp;Hairong Yuan","doi":"10.1007/s00021-025-00969-5","DOIUrl":"10.1007/s00021-025-00969-5","url":null,"abstract":"<div><p>This paper studies stationary supersonic compressible Euler flow in a two-dimensional finite straight nozzle. By introducing Glimm functionals with variable weights, we overcome the potential accumulation of successive reflections of weak waves between the two lateral walls, thus establish the existence of a weak entropy solution to a boundary-value problem of the Euler equations in the space of functions with bounded variations by a modified Glimm scheme.</p></div>","PeriodicalId":649,"journal":{"name":"Journal of Mathematical Fluid Mechanics","volume":"27 4","pages":""},"PeriodicalIF":1.3,"publicationDate":"2025-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144892443","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 Mixed Boundary Value Problems for the Steady Magnetohydrodynamics-Heat System with Joule Effects 具有焦耳效应的稳态磁流体动力-热系统的混合边值问题
IF 1.3 3区 数学
Journal of Mathematical Fluid Mechanics Pub Date : 2025-08-19 DOI: 10.1007/s00021-025-00968-6
Tujin Kim
{"title":"The Mixed Boundary Value Problems for the Steady Magnetohydrodynamics-Heat System with Joule Effects","authors":"Tujin Kim","doi":"10.1007/s00021-025-00968-6","DOIUrl":"10.1007/s00021-025-00968-6","url":null,"abstract":"<div><p>We are concerned with the steady Magnetohydrodynamics(MHD)-heat system with Joule effects under mixed boundary conditions. The boundary conditions for fluid may include the stick, pressure (or total pressure), vorticity, stress (or total stress) and friction types (Tresca slip, leak, one-sided leaks) boundary conditions together and for the electromagnetic field non-homogeneous mixed boundary conditions are given. The conditions for temperature may include non-homogeneous Dirichlet, Neumann and Robin conditions together. The viscosity, magnetic permeability, electrical conductivity, thermal conductivity and specific heat of the fluid depend on the temperature. The domain for fluid is not assumed to be simply connected. For the problem involving the static pressure and stress boundary conditions for fluid it is proved that if the parameter for buoyancy effect is small in accordance with the data of problem, a datum concerned with non-homogeneous mixed boundary conditions for magnetic field and the data of problem are small enough, then there exists a solution. For the problem involving the total pressure and total stress boundary conditions for fluid, the existence of a solution is proved when the parameter for buoyancy effect is small in accordance with the data of problem, a datum concerned with non-homogeneous mixed boundary conditions for magnetic field is small, but without the auxiliary smallness of the other data of problem. In addition (Appendix), a very simple proof of the fact that vorticity quadratic form for vector fields with mixed boundary conditions is positive-definite, which has been known in a previous paper and is used in this paper, is given.</p></div>","PeriodicalId":649,"journal":{"name":"Journal of Mathematical Fluid Mechanics","volume":"27 4","pages":""},"PeriodicalIF":1.3,"publicationDate":"2025-08-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144868797","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
Incompressible Navier–Stokes–Fourier Limit of the Steady Boltzmann Equation with Linear Boundary Condition in an Exterior Domain 外域线性边界条件下稳定Boltzmann方程的不可压缩Navier-Stokes-Fourier极限
IF 1.3 3区 数学
Journal of Mathematical Fluid Mechanics Pub Date : 2025-08-11 DOI: 10.1007/s00021-025-00965-9
Weijun Wu, Fujun Zhou, Yongsheng Li
{"title":"Incompressible Navier–Stokes–Fourier Limit of the Steady Boltzmann Equation with Linear Boundary Condition in an Exterior Domain","authors":"Weijun Wu,&nbsp;Fujun Zhou,&nbsp;Yongsheng Li","doi":"10.1007/s00021-025-00965-9","DOIUrl":"10.1007/s00021-025-00965-9","url":null,"abstract":"<div><p>This paper aims at justifying the incompressible Navier–Stokes–Fourier limit of the steady Boltzmann equation with linear boundary condition in an exterior domain. This generalizes the work Esposito, R., Guo, Y., Marra, R.: Hydrodynamic limit of a kinetic gas flow past an obstacle. Comm. Math. Phys. <b>364</b>, 765–823 (2018), to the non-isentropic case, in addition with a small external force and a small temperature variation between the wall and infinity. Some new estimates and a refined positivity-preserving scheme are established to construct a unique positive solution to the steady Boltzmann equation. An error estimate is also provided for the small Knudsen number.</p></div>","PeriodicalId":649,"journal":{"name":"Journal of Mathematical Fluid Mechanics","volume":"27 4","pages":""},"PeriodicalIF":1.3,"publicationDate":"2025-08-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144814528","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
Stability of Strong Solutions to the Full Compressible Magnetohydrodynamic System with Non-Conservative Boundary Conditions 非保守边界条件下全可压缩磁流体动力系统强解的稳定性
IF 1.3 3区 数学
Journal of Mathematical Fluid Mechanics Pub Date : 2025-08-06 DOI: 10.1007/s00021-025-00967-7
Hana Mizerová
{"title":"Stability of Strong Solutions to the Full Compressible Magnetohydrodynamic System with Non-Conservative Boundary Conditions","authors":"Hana Mizerová","doi":"10.1007/s00021-025-00967-7","DOIUrl":"10.1007/s00021-025-00967-7","url":null,"abstract":"<div><p>We define a dissipative measure-valued (DMV) solution to the system of equations governing the motion of a general compressible, viscous, electrically and heat conducting fluid driven by non-conservative boundary conditions. We show the stability of strong solutions to the full compressible magnetohydrodynamic system in a large class of these DMV solutions. In other words, we prove a DMV-strong uniqueness principle: a DMV solution coincides with the strong solution emanating from the same initial data as long as the latter exists.</p></div>","PeriodicalId":649,"journal":{"name":"Journal of Mathematical Fluid Mechanics","volume":"27 4","pages":""},"PeriodicalIF":1.3,"publicationDate":"2025-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00021-025-00967-7.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145162761","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
The Pressureless Damped Euler-Riesz System in the Critical Regularity Framework 临界正则框架下的无压阻尼Euler-Riesz系统
IF 1.3 3区 数学
Journal of Mathematical Fluid Mechanics Pub Date : 2025-08-05 DOI: 10.1007/s00021-025-00964-w
Meiling Chi, Ling-Yun Shou, Jiang Xu
{"title":"The Pressureless Damped Euler-Riesz System in the Critical Regularity Framework","authors":"Meiling Chi,&nbsp;Ling-Yun Shou,&nbsp;Jiang Xu","doi":"10.1007/s00021-025-00964-w","DOIUrl":"10.1007/s00021-025-00964-w","url":null,"abstract":"<div><p>We are concerned with a system governing the evolution of the pressureless compressible Euler equations with Riesz interaction and damping in <span>(mathbb {R}^{d})</span> (<span>(dge 1)</span>), where the interaction force is given by <span>(nabla (-Delta )^{(alpha -d)/2}rho )</span> with <span>(d-2&lt;alpha &lt;d)</span>. It is observed by the eigenvalue analysis that the density exhibits fractional heat diffusion behavior at low frequencies, which enables us to establish the global existence and large-time behavior of solutions to the Cauchy problem in the critical <span>(L^p)</span> framework. Precisely, the density and its <span>(sigma )</span>-order derivative converge to the equilibrium at the <span>(L^p)</span>-rate <span>((1+t)^{-(sigma -sigma _1)/(alpha -d+2)})</span> with <span>(-d/p-1le sigma _1&lt; d/p-1)</span>, consistent with the rate of solutions for the frictional heat equation. A non-local hypercoercivity argument and the effective unknown <span>(z=u+nabla Lambda ^{alpha -d}rho )</span> associated with the Darcy law are introduced to overcome the difficulty from the absence of hyperbolic symmetrization for first-order dissipative systems.</p></div>","PeriodicalId":649,"journal":{"name":"Journal of Mathematical Fluid Mechanics","volume":"27 4","pages":""},"PeriodicalIF":1.3,"publicationDate":"2025-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145162037","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
Three-Dimensional Flow of Ideal Fluid with Precessing Vortex Lines (Exact Solutions) 带涡线的理想流体三维流动（精确解）
IF 1.3 3区 数学
Journal of Mathematical Fluid Mechanics Pub Date : 2025-07-30 DOI: 10.1007/s00021-025-00962-y
A. A. Abrashkin
{"title":"Three-Dimensional Flow of Ideal Fluid with Precessing Vortex Lines (Exact Solutions)","authors":"A. A. Abrashkin","doi":"10.1007/s00021-025-00962-y","DOIUrl":"10.1007/s00021-025-00962-y","url":null,"abstract":"<div><p>Three-dimensional hydrodynamic equations of ideal incompressible fluid in Lagrangian form are considered. Their explicit solution is obtained. The trajectories of fluid particles are complex spatial curves depending on four frequencies. The vortex lines precess around the vertical axis. Their shape is determined by an arbitrary function depending on the axial Lagrangian coordinate. It is shown that the rotation axis is directed to the plane of vortex lines at some nonzero angle.</p></div>","PeriodicalId":649,"journal":{"name":"Journal of Mathematical Fluid Mechanics","volume":"27 3","pages":""},"PeriodicalIF":1.3,"publicationDate":"2025-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145171292","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
Weak Solution of One Navier’s Problem for the Stokes Resolvent System Stokes可解系统单Navier问题的弱解
IF 1.3 3区 数学
Journal of Mathematical Fluid Mechanics Pub Date : 2025-07-27 DOI: 10.1007/s00021-025-00959-7
Dagmar Medková
{"title":"Weak Solution of One Navier’s Problem for the Stokes Resolvent System","authors":"Dagmar Medková","doi":"10.1007/s00021-025-00959-7","DOIUrl":"10.1007/s00021-025-00959-7","url":null,"abstract":"<div><p>This paper studies the Stokes resolvent system <span>(-Delta textbf{u}+lambda textbf{u}+nabla rho =textbf{f})</span>, <span>(nabla cdot textbf{u}=chi )</span> in <span>(Omega )</span> with the Navier condition <span>(textbf{u}_textbf{n}=textbf{g}_textbf{n})</span>, <span>([partial textbf{u}/partial textbf{n}-rho textbf{n}+btextbf{u}]_tau =textbf{h}_tau )</span> on <span>(partial Omega )</span>. Here <span>(Omega subset {{mathbb {R}}}^2)</span> is a bounded domain with Lipschitz boundary. <span>(Omega )</span> might have holes. First we define and study weak solutions in <span>(W^{1,2}(Omega ;{{mathbb {C}}}^2)times L^2(Omega ;{{mathbb {C}}}))</span>. Using this result we are able to prove the existence of strong solutions of the problem in Sobolev spaces <span>(W^{s,q}(Omega ;{{mathbb {C}}}^2)times W^{s-1,q}(Omega ;{{mathbb {C}}}))</span>, in Besov spaces <span>(B_s^{q,r}(Omega ,{{mathbb {C}}}^2)times B_{s-1}^{q,r}(Omega ;{{mathbb {C}}}))</span> and classical solutions in the spaces <span>({{mathcal {C}}}^{k,alpha } ({overline{Omega }} ;{{mathbb {C}}}^2)times {{mathcal {C}}}^{k-1,alpha }({overline{Omega }} ;{{mathbb {C}}}))</span>.</p></div>","PeriodicalId":649,"journal":{"name":"Journal of Mathematical Fluid Mechanics","volume":"27 3","pages":""},"PeriodicalIF":1.3,"publicationDate":"2025-07-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145170328","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 Large Strong Solutions of Radially Symmetric Compressible MHD Equations in 2D Discs 二维圆盘上径向对称可压缩MHD方程的全局大强解
IF 1.3 3区 数学
Journal of Mathematical Fluid Mechanics Pub Date : 2025-07-24 DOI: 10.1007/s00021-025-00955-x
Xiangdi Huang, Weili Meng, Anchun Ni
{"title":"Global Large Strong Solutions of Radially Symmetric Compressible MHD Equations in 2D Discs","authors":"Xiangdi Huang,&nbsp;Weili Meng,&nbsp;Anchun Ni","doi":"10.1007/s00021-025-00955-x","DOIUrl":"10.1007/s00021-025-00955-x","url":null,"abstract":"<div><p>This paper is devoted to the study of the Dirichlet problem for the compressible magnetohydrodynamic system with density-dependent viscosities <span>(mu =const&gt;0,lambda =rho ^beta )</span> which was first introduced by Vaigant-Kazhikhov [18] in 1995. By assuming the endpoint case <span>(beta =1)</span> in the radially spherical symmetric setting, we establish the global existence to strong solution of the two-dimensional system for any large initial data. This also improves the previous work of Huang-Yan [10] where they proved the similar result for <span>(beta &gt;1)</span>. Our main idea is to utilize the geometric structure of a 2D spherically symmetric disc and the Sobolev critical embedding inequality of spherically symmetric functions in 2D domains, as well as a refined estimate of the upper bound of the density.</p></div>","PeriodicalId":649,"journal":{"name":"Journal of Mathematical Fluid Mechanics","volume":"27 3","pages":""},"PeriodicalIF":1.3,"publicationDate":"2025-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145168241","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 Existence and Non-Uniqueness of Global Weak Solution to a New Integrable System in (H^1(mathbb {R})) 一类新的可积系统整体弱解的存在性与非唯一性 (H^1(mathbb {R}))
IF 1.3 3区 数学
Journal of Mathematical Fluid Mechanics Pub Date : 2025-07-18 DOI: 10.1007/s00021-025-00963-x
Pei Zheng, Zhaoyang Yin
{"title":"The Existence and Non-Uniqueness of Global Weak Solution to a New Integrable System in (H^1(mathbb {R}))","authors":"Pei Zheng,&nbsp;Zhaoyang Yin","doi":"10.1007/s00021-025-00963-x","DOIUrl":"10.1007/s00021-025-00963-x","url":null,"abstract":"<div><p>In this paper, we establish the existence of the global weak admissible solution for the Cauchy problem of a <i>N</i>-peakon system in the sense of <span>(H^1(mathbb {R}))</span> space under a sign condition. Second, we claim that the global weak admissible solution for the system with the same initial data is not unique by giving a example. Finally, an image of the solutions of the above example which does not satisfy the uniqueness is given, which makes it easier to see the properties of non-uniqueness more intuitively.</p></div>","PeriodicalId":649,"journal":{"name":"Journal of Mathematical Fluid Mechanics","volume":"27 3","pages":""},"PeriodicalIF":1.3,"publicationDate":"2025-07-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145166405","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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