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Global Solutions to the Compressible Navier–Stokes-Poisson Equations with Slip Boundary Conditions in 3D Bounded Domains 三维有界区域中具有滑移边界条件的可压缩Navier-Stokes-Poisson方程的全局解
IF 1.2 3区 数学
Journal of Mathematical Fluid Mechanics Pub Date : 2025-03-19 DOI: 10.1007/s00021-025-00932-4
WenXue Wu
{"title":"Global Solutions to the Compressible Navier–Stokes-Poisson Equations with Slip Boundary Conditions in 3D Bounded Domains","authors":"WenXue Wu","doi":"10.1007/s00021-025-00932-4","DOIUrl":"10.1007/s00021-025-00932-4","url":null,"abstract":"<div><p>This paper concerns the initial-boundary-value problem of the compressible Navier-Stokes-Poisson equations subject to large and non-flat doping profile in 3D bounded domain, where the velocity admits slip boundary condition. The global existence of strong solutions and smooth solutions near a steady state for compressible NSP are established by using the energy estimates. In particular, an important feature is that the steady state (except velocity) and the doping profile are allowed to be large.</p></div>","PeriodicalId":649,"journal":{"name":"Journal of Mathematical Fluid Mechanics","volume":"27 2","pages":""},"PeriodicalIF":1.2,"publicationDate":"2025-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143645552","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 Inviscid Limit Connecting Brinkman’s and Darcy’s Models of Tissue Growth with Nonlinear Pressure 非线性压力下Brinkman和Darcy组织生长模型的无粘极限
IF 1.2 3区 数学
Journal of Mathematical Fluid Mechanics Pub Date : 2025-03-17 DOI: 10.1007/s00021-025-00933-3
Charles Elbar, Jakub Skrzeczkowski
{"title":"On the Inviscid Limit Connecting Brinkman’s and Darcy’s Models of Tissue Growth with Nonlinear Pressure","authors":"Charles Elbar,&nbsp;Jakub Skrzeczkowski","doi":"10.1007/s00021-025-00933-3","DOIUrl":"10.1007/s00021-025-00933-3","url":null,"abstract":"<div><p>Several recent papers have addressed the modelling of tissue growth by multi-phase models where the velocity is related to the pressure by one of the physical laws (Stokes’, Brinkman’s or Darcy’s). While each of these models has been extensively studied, not so much is known about the connection between them. In the recent paper (David et al. in SIAM J. Math. Anal. 56(2):2090–2114, 2024), assuming the linear form of the pressure, the Authors connected two multi-phase models by an inviscid limit: the viscoelastic one (of Brinkman’s type) and the inviscid one (of Darcy’s type). Here, we prove that the same is true for a nonlinear, power-law pressure. The new ingredient is that we use the relation between the pressure <i>p</i> and the Brinkman potential <i>W</i> to deduce compactness in space of <i>p</i> from the compactness in space of <i>W</i>.</p></div>","PeriodicalId":649,"journal":{"name":"Journal of Mathematical Fluid Mechanics","volume":"27 2","pages":""},"PeriodicalIF":1.2,"publicationDate":"2025-03-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00021-025-00933-3.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143632497","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
(L^{r})-Results of the Stationary Navier–Stokes Equations with Nonzero Velocity at Infinity (L^{r})-无穷远处非零速度的平稳Navier-Stokes方程的结果
IF 1.2 3区 数学
Journal of Mathematical Fluid Mechanics Pub Date : 2025-03-14 DOI: 10.1007/s00021-025-00921-7
Dugyu Kim
{"title":"(L^{r})-Results of the Stationary Navier–Stokes Equations with Nonzero Velocity at Infinity","authors":"Dugyu Kim","doi":"10.1007/s00021-025-00921-7","DOIUrl":"10.1007/s00021-025-00921-7","url":null,"abstract":"<div><p>We study the stationary motion of an incompressible Navier–Stokes fluid past obstacles in <span>(mathbb {R}^{3})</span>, subject to the provided boundary velocity <span>(u_{b})</span>, external force <span>(f = textrm{div} F)</span>, and nonzero constant vector <span>(k {e_1})</span> at infinity. We first prove that the existence of at least one very weak solution <i>u</i> in <span>(L^{3}(Omega ) + L^{4}(Omega ))</span> for an arbitrary large <span>(F in L^{3/2}(Omega ) + L^{2}(Omega ))</span> provided that the flux of <span>(u_{b})</span> on the boundary of each body is sufficiently small with respect to the viscosity <span>(nu )</span>. Moreover, we establish weak- and strong-regularity results for very weak solutions. Consequently, our existence and regularity results enable us to prove the existence of a weak solution satisfying <span>(nabla u in L^{r}(Omega ))</span> for a given <span>(F in L^{r}(Omega ))</span> with <span>(3/2 le r le 2)</span>, and a strong solution satisfying <span>(nabla ^{2} u in L^{s}(Omega ))</span> for a given <span>(f in L^{s}(Omega ))</span> with <span>(1 &lt; s le 6/5)</span>, respectively.</p></div>","PeriodicalId":649,"journal":{"name":"Journal of Mathematical Fluid Mechanics","volume":"27 2","pages":""},"PeriodicalIF":1.2,"publicationDate":"2025-03-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143612265","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
Partial Regularity for Navier-Stokes Equations 纳维-斯托克斯方程的部分正则性
IF 1.2 3区 数学
Journal of Mathematical Fluid Mechanics Pub Date : 2025-03-06 DOI: 10.1007/s00021-025-00929-z
Lihe Wang
{"title":"Partial Regularity for Navier-Stokes Equations","authors":"Lihe Wang","doi":"10.1007/s00021-025-00929-z","DOIUrl":"10.1007/s00021-025-00929-z","url":null,"abstract":"<div><p>Using a more geometric approach, we demonstrate that the solutions to the Navier–Stokes equations remain regular except on a set with a null Hausdorff measure of dimension 1. The proof primarily relies on a new compactness lemma and the monotonicity property of harmonic functions. The combination of linear and nonlinear approximation schemes makes the proof clear and transparent.</p></div>","PeriodicalId":649,"journal":{"name":"Journal of Mathematical Fluid Mechanics","volume":"27 2","pages":""},"PeriodicalIF":1.2,"publicationDate":"2025-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143564420","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 Rough Calderón Solutions to the Navier–Stokes Equations and Applications to the Singular Set Navier-Stokes方程的粗糙Calderón解及其在奇异集上的应用
IF 1.2 3区 数学
Journal of Mathematical Fluid Mechanics Pub Date : 2025-03-04 DOI: 10.1007/s00021-025-00930-6
Henry Popkin
{"title":"On Rough Calderón Solutions to the Navier–Stokes Equations and Applications to the Singular Set","authors":"Henry Popkin","doi":"10.1007/s00021-025-00930-6","DOIUrl":"10.1007/s00021-025-00930-6","url":null,"abstract":"<div><p>In 1934, Leray (Acta Math 63:193–248, 1934) proved the existence of global-in-time weak solutions to the Navier–Stokes equations for any divergence-free initial data in <span>(L^2(mathbb {R}^3))</span>. In the 1980s, Giga (J Differ Equ 62(2):186–212, 1986) and Kato (Math Z 187(4):471–480, 1984) independently showed that there exist global-in-time mild solutions corresponding to small enough critical <span>(L^3(mathbb {R}^3))</span> initial data. In 1990, Calderón (Trans Am Math Soc 318:179–200, 1990) filled the gap to show that there exist global-in-time weak solutions for all supercritical initial data in <span>(L^p(mathbb {R}^3))</span> for <span>(2&lt; p&lt;3)</span> by utilising a splitting argument, blending the constructions of Leray and Giga-Kato. In this paper, we utilise a “Calderón-like” splitting to show the global-in-time existence of weak solutions to the Navier–Stokes equations corresponding to supercritical Besov space initial data <span>(u_0 in dot{B}^{s}_{{q},{infty }}(mathbb {R}^3))</span> where <span>(q&gt;2)</span> and <span>(-1+frac{2}{q}&lt;s&lt;min left( -1+frac{3}{q},0 right) )</span>, which fills a similar gap between Leray and known mild solution theory in the Besov space setting. We also use the Calderón-like splitting to investigate the structure of the singular set under a Type-I blow-up assumption in the Besov space setting, which is considerably rougher than in previous works.</p></div>","PeriodicalId":649,"journal":{"name":"Journal of Mathematical Fluid Mechanics","volume":"27 2","pages":""},"PeriodicalIF":1.2,"publicationDate":"2025-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00021-025-00930-6.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143553918","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 Navier–Stokes Cauchy Problem in a Class of Weighted Function Spaces 一类加权函数空间中的Navier-Stokes Cauchy问题
IF 1.2 3区 数学
Journal of Mathematical Fluid Mechanics Pub Date : 2025-02-20 DOI: 10.1007/s00021-025-00923-5
Paolo Maremonti, Vittorio Pane
{"title":"The Navier–Stokes Cauchy Problem in a Class of Weighted Function Spaces","authors":"Paolo Maremonti,&nbsp;Vittorio Pane","doi":"10.1007/s00021-025-00923-5","DOIUrl":"10.1007/s00021-025-00923-5","url":null,"abstract":"<div><p>We consider the Navier–Stokes Cauchy problem with an initial datum in a weighted Lebesgue space. The weight is a radial function increasing at infinity. Our study partially follows the ideas of the paper by Galdi and Maremonti (J Math Fluid Mech 25:7, 2023). The authors of the quoted paper consider a special study of stability of steady fluid motions. The results hold in 3D and for small data. Here, relatively to the perturbations of the rest state, we generalize the result. We study the <i>n</i>D Navier–Stokes Cauchy problem, <span>(nge 3)</span>. We prove the existence (local) of a unique regular solution. Moreover, the solution enjoys a spatial asymptotic decay whose order of decay is connected to the weight.</p></div>","PeriodicalId":649,"journal":{"name":"Journal of Mathematical Fluid Mechanics","volume":"27 2","pages":""},"PeriodicalIF":1.2,"publicationDate":"2025-02-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143455670","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
Sharp Interface Limit for Compressible Immiscible Two-Phase Dynamics with Relaxation 带松弛的可压缩非混相两相动力学的锐界面极限
IF 1.2 3区 数学
Journal of Mathematical Fluid Mechanics Pub Date : 2025-02-18 DOI: 10.1007/s00021-025-00927-1
Yazhou Chen, Yi Peng, Qiaolin He, Xiaoding Shi
{"title":"Sharp Interface Limit for Compressible Immiscible Two-Phase Dynamics with Relaxation","authors":"Yazhou Chen,&nbsp;Yi Peng,&nbsp;Qiaolin He,&nbsp;Xiaoding Shi","doi":"10.1007/s00021-025-00927-1","DOIUrl":"10.1007/s00021-025-00927-1","url":null,"abstract":"<div><p>In this paper, the sharp interface limit for compressible Navier–Stokes/Allen-Cahn system with relaxation is investigated, which is motivated by the Jin-Xin relaxation scheme ([Comm.Pure Appl.Math.,48,1995]). Given any entropy solution which consists of two different families of shocks interacting at some positive time for the immiscible two-phase compressible Euler equations, it is proved that such entropy solution is the singular limit for a family global strong solutions of the compressible Navier–Stokes/Allen-Cahn system with relaxation when the interface thickness of immiscible two-phase flow tends to zero. The weighted estimation and improved anti-derivative method are used in the proof. The results of this singular limit show that, the sharp interface limit of the compressible Navier–Stokes/Allen-Cahn system with relaxation is the immiscible two-phase compressible Euler equations with free interface between phases. Moreover, the interaction of shock waves belong to different families can pass through the two-phase flow interface and maintain the wave strength and wave speed without being affected by the interface for immiscible compressible two-phase flow.</p></div>","PeriodicalId":649,"journal":{"name":"Journal of Mathematical Fluid Mechanics","volume":"27 2","pages":""},"PeriodicalIF":1.2,"publicationDate":"2025-02-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143438575","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
Liouville Type Theorems for the Stationary Navier–Stokes Equations in High-Dimension Without Vanishing Condition 高维无消失条件下平稳Navier-Stokes方程的Liouville型定理
IF 1.2 3区 数学
Journal of Mathematical Fluid Mechanics Pub Date : 2025-02-12 DOI: 10.1007/s00021-025-00925-3
Huiting Ding
{"title":"Liouville Type Theorems for the Stationary Navier–Stokes Equations in High-Dimension Without Vanishing Condition","authors":"Huiting Ding","doi":"10.1007/s00021-025-00925-3","DOIUrl":"10.1007/s00021-025-00925-3","url":null,"abstract":"<div><p>The Liouville theorem for smooth solutions with finite Dirichlet integrals and uniform vanishing conditions to high-dimension stationary Navier–Stokes equations was established as reported by Galdi (An introduction to the mathematical theory of the Navier–Stokes equations: Steady-state problems, Springer, New York, 2011). In this paper, we mainly concern with the Liouville type problem of weak solutions only with finite Dirichlet integral to the stationary Navier–Stokes equations on <span>(mathbb {R}^d)</span> with <span>(dge 5)</span>. We first establish a Liouville type theorem under some restrictions on the high-frequency part tending to infinity of velocity fields. Then, we show the uniqueness of weak solutions to the stationary fractional Navier–Stokes equations with finite critical Dirichlet integral by establishing another Liouville type theorem.</p></div>","PeriodicalId":649,"journal":{"name":"Journal of Mathematical Fluid Mechanics","volume":"27 2","pages":""},"PeriodicalIF":1.2,"publicationDate":"2025-02-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143396579","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
Grad-Div Stabilized Finite Element Method for Magnetohydrodynamic Flows at Low Magnetic Reynolds Numbers 低磁雷诺数磁流体的 Grad-Div 稳定有限元法
IF 1.2 3区 数学
Journal of Mathematical Fluid Mechanics Pub Date : 2025-02-12 DOI: 10.1007/s00021-025-00920-8
Yao Rong, Feng Shi, Yi Li, Yuhong Zhang
{"title":"Grad-Div Stabilized Finite Element Method for Magnetohydrodynamic Flows at Low Magnetic Reynolds Numbers","authors":"Yao Rong,&nbsp;Feng Shi,&nbsp;Yi Li,&nbsp;Yuhong Zhang","doi":"10.1007/s00021-025-00920-8","DOIUrl":"10.1007/s00021-025-00920-8","url":null,"abstract":"<div><p>The divergence constraint of the incompressible fluids usually causes the weak robustness of standard mixed finite element methods. Grad-div stabilization is a popular technique for improving the robustness. In this paper, we theoretically show that for magnetohydrodynamic flows at large Hartmann numbers, grad-div stabilization can improve the well-posedness and robust stability of the continuous problem, and remove the effect of Hartmann number on the finite element discrete errors. Besides, applying the backward Euler method and lagging the nonlinear term, we construct a linear grad-div stabilized finite element algorithm for magnetohydrodynamics flows at low magnetic Reynolds numbers. A complete theoretical analysis of its stability and convergency is provided. Some computational experiments illustrate the validness of our algorithm and its theoretical results and also the benefits of grad-div stabilization.</p></div>","PeriodicalId":649,"journal":{"name":"Journal of Mathematical Fluid Mechanics","volume":"27 2","pages":""},"PeriodicalIF":1.2,"publicationDate":"2025-02-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143396620","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
Gevrey Type Error Estimates of Solutions to the Navier–Stokes Equations Navier-Stokes方程解的Gevrey型误差估计
IF 1.2 3区 数学
Journal of Mathematical Fluid Mechanics Pub Date : 2025-02-07 DOI: 10.1007/s00021-025-00924-4
Yuta Koizumi
{"title":"Gevrey Type Error Estimates of Solutions to the Navier–Stokes Equations","authors":"Yuta Koizumi","doi":"10.1007/s00021-025-00924-4","DOIUrl":"10.1007/s00021-025-00924-4","url":null,"abstract":"<div><p>Consider the Cauchy problem of the Navier–Stokes equations in <span>(mathbb {R}^n (n ge 2))</span> with the initial data <span>(a in dot{B}^{-1+n/p}_{p, infty })</span> for <span>(n&lt; p &lt; infty )</span>. We establish the Gevrey type estimates for the error between the successive approximations <span>({u_j}_{j=0}^{infty })</span> and the strong solution <i>u</i> provided the convergence in the scaling invariant norm in <span>(L^q(mathbb {R}^n))</span> with the time weight holds. It is also clarified that the convergence rate of the higher order approximation is at least the same as that of the lower order approximation. In addition, the approximation for the pressure is also established.</p></div>","PeriodicalId":649,"journal":{"name":"Journal of Mathematical Fluid Mechanics","volume":"27 2","pages":""},"PeriodicalIF":1.2,"publicationDate":"2025-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143361913","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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