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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
(W^{2,p})-Estimates of the Stokes System with Traction Boundary Conditions (W^{2,p})-具有牵引边界条件的Stokes系统的估计
IF 1.2 3区 数学
Journal of Mathematical Fluid Mechanics Pub Date : 2025-04-18 DOI: 10.1007/s00021-025-00934-2
Paul Deuring
{"title":"(W^{2,p})-Estimates of the Stokes System with Traction Boundary Conditions","authors":"Paul Deuring","doi":"10.1007/s00021-025-00934-2","DOIUrl":"10.1007/s00021-025-00934-2","url":null,"abstract":"<div><p>The article deals with the 3D stationary Stokes system under traction boundary conditions, in interior and exterior domains. In the interior domain case, we obtain solutions with <span>(W^{2,p})</span>-regular velocity and <span>(W^{1,p})</span>-regular pressure globally in the domain, under suitable assumptions on the data. In the exterior domain case we construct two solutions classes, both of them consisting of functions which are <span>(W^{2,p})</span>–<span>(W^{1,p})</span>-regular in any vicinity of the boundary, with <span>(p in (1, infty ))</span> determined by the assumptions on the data. In addition the velocity part of these solutions is <span>(L^s)</span>-integrable near infinity, for some <span>(s&gt;3)</span>, provided that the right-hand side of the Stokes system is <span>(L^p)</span>-integrable near infinity for some <span>(p&lt;3/2)</span>. Moreover, the velocity part of the solutions in one of the two classes satisfies a zero flux condition on the boundary, whereas the pressure part of the solutions in the other class is <span>(L^s)</span>-integrable near infinity, for some <span>(s &gt; 3/2)</span>. The two solution classes are also uniqueness classes, one related to a zero flux condition for the velocity, the other one to decay of the pressure at infinity. This result confirms a conjecture by T. Hishida (University of Nagoya).</p></div>","PeriodicalId":649,"journal":{"name":"Journal of Mathematical Fluid Mechanics","volume":"27 2","pages":""},"PeriodicalIF":1.2,"publicationDate":"2025-04-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143848936","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
Combination of Osgood and Nagumo-Type Uniqueness for Nonlinear Differential Equations 非线性微分方程的Osgood和nagumo型唯一性组合
IF 1.2 3区 数学
Journal of Mathematical Fluid Mechanics Pub Date : 2025-03-28 DOI: 10.1007/s00021-025-00935-1
Ke Jiang, Sulei Wang
{"title":"Combination of Osgood and Nagumo-Type Uniqueness for Nonlinear Differential Equations","authors":"Ke Jiang,&nbsp;Sulei Wang","doi":"10.1007/s00021-025-00935-1","DOIUrl":"10.1007/s00021-025-00935-1","url":null,"abstract":"<div><p>We show that a convex combination of the Osgood and Nagumo conditions ensures the uniqueness of the solution to the boundary value problem for a second-order nonlinear differential equation on a semi-infinite interval. A typical example of such problem is a recently derived nonlinear model for the motion of arctic gyres.</p></div>","PeriodicalId":649,"journal":{"name":"Journal of Mathematical Fluid Mechanics","volume":"27 2","pages":""},"PeriodicalIF":1.2,"publicationDate":"2025-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143716987","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
Multidimensional Stability and Transverse Bifurcation of Hydraulic Shocks and Roll Waves in Open Channel Flow 明渠水流中液压冲击和横摇波的多维稳定性和横向分岔
IF 1.2 3区 数学
Journal of Mathematical Fluid Mechanics Pub Date : 2025-03-19 DOI: 10.1007/s00021-025-00928-0
Zhao Yang, Kevin Zumbrun
{"title":"Multidimensional Stability and Transverse Bifurcation of Hydraulic Shocks and Roll Waves in Open Channel Flow","authors":"Zhao Yang,&nbsp;Kevin Zumbrun","doi":"10.1007/s00021-025-00928-0","DOIUrl":"10.1007/s00021-025-00928-0","url":null,"abstract":"<div><p>We study by a combination of analytical and numerical methods multidimensional stability and transverse bifurcation of planar hydraulic shock and roll wave solutions of the inviscid Saint Venant equations for inclined shallow-water flow, both in the whole space and in a channel of finite width, obtaining complete stability diagrams across the full parameter range of existence. Technical advances include development of efficient multi-d Evans solvers, low- and high-frequency asymptotics, explicit/semi-explicit computation of stability boundaries, and rigorous treatment of channel flow with wall-type physical boundary. Notable behavioral phenomena are a novel essential transverse bifurcation of hydraulic shocks to invading planar periodic roll-wave or doubly-transverse periodic herringbone patterns, with associated metastable behavior driven by mixed roll- and herringbone-type waves initiating from localized perturbation of an unstable constant state; and Floquet-type transverse “flapping” bifurcation of roll wave patterns.\u0000</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":"143645498","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 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
Homogenization of Non-Homogeneous Incompressible Navier–Stokes System in Critically Perforated Domains 临界穿孔区域非齐次不可压缩Navier-Stokes系统的均匀化
IF 1.2 3区 数学
Journal of Mathematical Fluid Mechanics Pub Date : 2025-03-04 DOI: 10.1007/s00021-025-00931-5
Jiaojiao Pan
{"title":"Homogenization of Non-Homogeneous Incompressible Navier–Stokes System in Critically Perforated Domains","authors":"Jiaojiao Pan","doi":"10.1007/s00021-025-00931-5","DOIUrl":"10.1007/s00021-025-00931-5","url":null,"abstract":"<div><p>In this paper, we study the homogenization of 3<i>D</i> non-homogeneous incompressible Navier–Stokes system in perforated domains with holes of critical size. Under very mild assumptions concerning the shape of the obstacles and their mutual distance, we show that when <span>(varepsilon rightarrow 0)</span>, the velocity and density converge to a solution of the non-homogeneous incompressible Navier–Stokes system with a friction term of Brinkman type.</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":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143553643","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
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