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Note on global stability of 2D anisotropic Boussinesq equations near the hydrostatic equilibrium 二维各向异性Boussinesq方程在流体静力平衡附近的全局稳定性
IF 1.8 3区 数学
Nonlinear Analysis-Real World Applications Pub Date : 2025-03-22 DOI: 10.1016/j.nonrwa.2025.104370
Hua Qiu, Xia Wang
{"title":"Note on global stability of 2D anisotropic Boussinesq equations near the hydrostatic equilibrium","authors":"Hua Qiu,&nbsp;Xia Wang","doi":"10.1016/j.nonrwa.2025.104370","DOIUrl":"10.1016/j.nonrwa.2025.104370","url":null,"abstract":"<div><div>In this note, we consider the stability problem of the 2D anisotropic Boussinesq equations near the hydrostatic equilibrium. Precisely, we obtain the global stability of smooth solution for the 2D Boussinesq equations with partial dissipation and horizontal diffusion in sense of <span><math><msup><mrow><mi>H</mi></mrow><mrow><mn>3</mn></mrow></msup></math></span>. Our result extends the recent stability results in Ji et al., (2019), Wei et al., (2021), Chen and Liu (2022).</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"85 ","pages":"Article 104370"},"PeriodicalIF":1.8,"publicationDate":"2025-03-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143680442","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
Existence and convergence analysis of second-order delay differential variational–hemivariational inequalities with memory terms 具有记忆项的二阶时滞微分变分-半变分不等式的存在性与收敛性分析
IF 1.8 3区 数学
Nonlinear Analysis-Real World Applications Pub Date : 2025-03-21 DOI: 10.1016/j.nonrwa.2025.104373
Jianwei Hao , Jiangfeng Han , Quansheng Liu
{"title":"Existence and convergence analysis of second-order delay differential variational–hemivariational inequalities with memory terms","authors":"Jianwei Hao ,&nbsp;Jiangfeng Han ,&nbsp;Quansheng Liu","doi":"10.1016/j.nonrwa.2025.104373","DOIUrl":"10.1016/j.nonrwa.2025.104373","url":null,"abstract":"<div><div>This study conducts an investigation into a generalized second-order delay differentialvariational–hemivariational inequality (SDVHI), formulated as a coupled system comprising a variational–hemivariational inequality with memory terms and a second-order delay differential equation. Initially, we establish the well-posedness of the system, proving the existence and uniqueness of solutions. Subsequently, we analyze the convergence properties of the SDVHI solutions. The practical applicability and relevance of the theoretical insights are demonstrated through a parabolic–elliptic system with an obstacle, highlighting the study’s contributions to the field.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"85 ","pages":"Article 104373"},"PeriodicalIF":1.8,"publicationDate":"2025-03-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143680441","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
Optimality of smallness conditions in Willmore obstacle problems under Dirichlet boundary conditions Dirichlet边界条件下Willmore障碍问题小条件的最优性
IF 1.8 3区 数学
Nonlinear Analysis-Real World Applications Pub Date : 2025-03-14 DOI: 10.1016/j.nonrwa.2025.104363
Hans-Christoph Grunau , Shinya Okabe
{"title":"Optimality of smallness conditions in Willmore obstacle problems under Dirichlet boundary conditions","authors":"Hans-Christoph Grunau ,&nbsp;Shinya Okabe","doi":"10.1016/j.nonrwa.2025.104363","DOIUrl":"10.1016/j.nonrwa.2025.104363","url":null,"abstract":"<div><div>We consider the obstacle problem under Dirichlet boundary conditions for Euler’s elastica functional in the class of one-dimensional symmetric graphs over the real axis. We prove the optimality of a previously obtained smallness condition on the size of obstacles such that the obstacle problem possesses a minimiser.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"85 ","pages":"Article 104363"},"PeriodicalIF":1.8,"publicationDate":"2025-03-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143620265","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
Enhanced dissipation and temporal decay in the Euler–Poisson–Navier–Stokes equations 欧拉-泊松-纳维-斯托克斯方程的增强耗散和时间衰减
IF 1.8 3区 数学
Nonlinear Analysis-Real World Applications Pub Date : 2025-03-14 DOI: 10.1016/j.nonrwa.2025.104365
Young-Pil Choi , Houzhi Tang , Weiyuan Zou
{"title":"Enhanced dissipation and temporal decay in the Euler–Poisson–Navier–Stokes equations","authors":"Young-Pil Choi ,&nbsp;Houzhi Tang ,&nbsp;Weiyuan Zou","doi":"10.1016/j.nonrwa.2025.104365","DOIUrl":"10.1016/j.nonrwa.2025.104365","url":null,"abstract":"<div><div>This paper investigates the global well-posedness and large-time behavior of solutions for a coupled fluid model in <span><math><msup><mrow><mi>R</mi></mrow><mrow><mn>3</mn></mrow></msup></math></span> consisting of the isothermal compressible Euler–Poisson system and incompressible Navier–Stokes equations coupled through the drag force. Notably, we exploit the dissipation effects inherent in the Poisson equation to achieve a faster decay of fluid density compared to velocities. This strategic utilization of dissipation, together with the influence of the electric field and the damping structure induced by the drag force, leads to a remarkable decay behavior: the fluid density converges to equilibrium at a rate of <span><math><msup><mrow><mrow><mo>(</mo><mn>1</mn><mo>+</mo><mi>t</mi><mo>)</mo></mrow></mrow><mrow><mo>−</mo><mn>11</mn><mo>/</mo><mn>4</mn></mrow></msup></math></span>, significantly faster than the decay rates of velocity differences <span><math><msup><mrow><mrow><mo>(</mo><mn>1</mn><mo>+</mo><mi>t</mi><mo>)</mo></mrow></mrow><mrow><mo>−</mo><mn>7</mn><mo>/</mo><mn>4</mn></mrow></msup></math></span> and velocities themselves <span><math><msup><mrow><mrow><mo>(</mo><mn>1</mn><mo>+</mo><mi>t</mi><mo>)</mo></mrow></mrow><mrow><mo>−</mo><mn>3</mn><mo>/</mo><mn>4</mn></mrow></msup></math></span> in the <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> norm. Furthermore, under the condition of vanishing coupled incompressible flow, we demonstrate an exponential decay to a constant state for the solution of the corresponding system, the damped Euler–Poisson system.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"85 ","pages":"Article 104365"},"PeriodicalIF":1.8,"publicationDate":"2025-03-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143620264","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
A Hyperbolic–parabolic framework to manage traffic generated pollution 管理交通污染的双曲-抛物线框架
IF 1.8 3区 数学
Nonlinear Analysis-Real World Applications Pub Date : 2025-03-13 DOI: 10.1016/j.nonrwa.2025.104361
Rinaldo M. Colombo , Paola Goatin , Elena Rossi
{"title":"A Hyperbolic–parabolic framework to manage traffic generated pollution","authors":"Rinaldo M. Colombo ,&nbsp;Paola Goatin ,&nbsp;Elena Rossi","doi":"10.1016/j.nonrwa.2025.104361","DOIUrl":"10.1016/j.nonrwa.2025.104361","url":null,"abstract":"<div><div>Vehicular traffic flows through a merge regulated by traffic lights and produces pollutant that diffuses in the surrounding region. This situation motivates a general hyperbolic - parabolic system, whose well-posedness and stability are here proved in <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span>. Roads are allowed to be also 2-dimensional. The effects of stop &amp; go waves are comprised, leading to measure source terms in the parabolic equation. The traffic lights, as well as inflows and outflows, can be regulated to minimize the presence of pollutant in given regions.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"85 ","pages":"Article 104361"},"PeriodicalIF":1.8,"publicationDate":"2025-03-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143620360","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
Existence of weak solutions for nonisothermal immiscible compressible two-phase flow in porous media 多孔介质中非等温非混溶可压缩两相流弱解的存在性
IF 1.8 3区 数学
Nonlinear Analysis-Real World Applications Pub Date : 2025-03-12 DOI: 10.1016/j.nonrwa.2025.104364
B. Amaziane , M. Jurak , L. Pankratov , A. Piatnitski
{"title":"Existence of weak solutions for nonisothermal immiscible compressible two-phase flow in porous media","authors":"B. Amaziane ,&nbsp;M. Jurak ,&nbsp;L. Pankratov ,&nbsp;A. Piatnitski","doi":"10.1016/j.nonrwa.2025.104364","DOIUrl":"10.1016/j.nonrwa.2025.104364","url":null,"abstract":"<div><div>We introduce a model of the time evolution of a flow of immiscible compressible fluids in porous media, taking into account the thermal effects. The problem leads to a coupled system of three nonlinear equations, two of which are degenerate. The time derivative has a new degeneracy in addition to the usual one in two-phase flows because of compressibility. We introduce a suitable weak formulation of the problem based on the total energy conservation principle. A new existence result of weak solutions of the more general model is obtained based on assumptions that are physically relevant to the problem data. The result is obtained in several steps involving an appropriate regularization and a time discretization. First we prove the existence of a weak solution for the non-degenerate problem based on obtaining a priori estimates, discrete maximum principle, and using the Leray–Schauder fixed point theorem. Finally, by using uniform estimates, our compactness result, and a suitable limit passages, we can establish the existence of a weak solution to the degenerate problem. This result is a further progress compared to the result obtained in [Math. Methods Appl. Sci. 40 (2017), no. 18, 7510–7539.], which deals with an incompressible model.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"85 ","pages":"Article 104364"},"PeriodicalIF":1.8,"publicationDate":"2025-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143601017","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
Numerical analysis of a class of hemivariational inequalities governed by fluid–fluid coupled flow 一类流体-流体耦合流动控制的半变分不等式的数值分析
IF 1.8 3区 数学
Nonlinear Analysis-Real World Applications Pub Date : 2025-03-11 DOI: 10.1016/j.nonrwa.2025.104366
Feifei Jing , Weimin Han , Guanyu Zhou
{"title":"Numerical analysis of a class of hemivariational inequalities governed by fluid–fluid coupled flow","authors":"Feifei Jing ,&nbsp;Weimin Han ,&nbsp;Guanyu Zhou","doi":"10.1016/j.nonrwa.2025.104366","DOIUrl":"10.1016/j.nonrwa.2025.104366","url":null,"abstract":"<div><div>We explore the well-posedness and conduct a numerical analysis of hemivariational inequalities for the coupled stationary Navier–Stokes/Navier–Stokes system. The interface condition involves the Clark subgradient and serves as a generalization of various interface interaction relations, including nonlinear transmission conditions and friction-type conditions. We present an existence and uniqueness result for a solution of the continuous model. We propose a domain decomposition approach to solve the coupled system and examine the convergence of iterations. Moreover, we use the finite element approximation to discretize the hemivariational inequality of the coupled system and derive error estimates, which lead to an optimal order for the <span><math><mrow><mi>P</mi><mn>1</mn><mi>b</mi></mrow></math></span>/<span><math><mrow><mi>P</mi><mn>1</mn></mrow></math></span> pair under appropriate solution regularity assumptions. Numerical results are reported that illustrate the optimal convergence order predicted by theoretical analysis.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"85 ","pages":"Article 104366"},"PeriodicalIF":1.8,"publicationDate":"2025-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143592411","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 onset of wave-breaking and the time evolution of the maximum of horizontal velocity in rotational equatorial waves 旋赤道波的破波起始和最大水平速度的时间演化
IF 1.8 3区 数学
Nonlinear Analysis-Real World Applications Pub Date : 2025-03-11 DOI: 10.1016/j.nonrwa.2025.104367
Calin I. Martin
{"title":"On the onset of wave-breaking and the time evolution of the maximum of horizontal velocity in rotational equatorial waves","authors":"Calin I. Martin","doi":"10.1016/j.nonrwa.2025.104367","DOIUrl":"10.1016/j.nonrwa.2025.104367","url":null,"abstract":"<div><div>We are concerned here with the time evolution of the maximal (modified) surface velocity for a rotational wave in the <span><math><mi>f</mi></math></span>-plane approximation. Using a parametric description of the wave surface, we show that the appearance of asymmetry in the wave profile is a necessary condition for the occurrence of a fluid velocity that exceeds the wave crest celerity, the latter occurence characterizing the inception of the wave-breaking phenomenon. This is achieved by means of an equation relating the time evolution of the maximum of the (modified) horizontal velocity to the horizontal component of the pressure gradient. Our analysis extends previous results concerning irrotational flows to the rotational situation of constant vorticity.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"85 ","pages":"Article 104367"},"PeriodicalIF":1.8,"publicationDate":"2025-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143592409","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 Riemann problem for a generalised Burgers equation with spatially decaying sound speed. II General qualitative theory and numerical analysis 具有空间衰减声速的广义Burgers方程的黎曼问题。一般定性理论和数值分析
IF 1.8 3区 数学
Nonlinear Analysis-Real World Applications Pub Date : 2025-03-11 DOI: 10.1016/j.nonrwa.2025.104349
John Christopher Meyer, David John Needham
{"title":"The Riemann problem for a generalised Burgers equation with spatially decaying sound speed. II General qualitative theory and numerical analysis","authors":"John Christopher Meyer,&nbsp;David John Needham","doi":"10.1016/j.nonrwa.2025.104349","DOIUrl":"10.1016/j.nonrwa.2025.104349","url":null,"abstract":"<div><div>In this paper, we establish the global well-posedness of the Cauchy problem for a generalised viscous Burgers equation with spatially decaying sound speed, continuing from part I of this series of papers. Moreover, we establish qualitative properties, specifically bounds and monotonicity properties of solutions to the Cauchy problem. We also establish a conditional convergence result for an explicit mid-point finite difference scheme used throughout part I to approximate solutions to the Cauchy problem.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"85 ","pages":"Article 104349"},"PeriodicalIF":1.8,"publicationDate":"2025-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143592410","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
Nonlinear mountain waves with active precipitation 具有活跃降水的非线性山波
IF 1.8 3区 数学
Nonlinear Analysis-Real World Applications Pub Date : 2025-03-10 DOI: 10.1016/j.nonrwa.2025.104351
Tony Lyons
{"title":"Nonlinear mountain waves with active precipitation","authors":"Tony Lyons","doi":"10.1016/j.nonrwa.2025.104351","DOIUrl":"10.1016/j.nonrwa.2025.104351","url":null,"abstract":"<div><div>Exact nonlinear mountain waves described using Lagrangian variables are considered with constant enthalpy of vapourisation in a moist atmosphere. It is shown that if a streamline in the flow with a given temperature is saturated, then the dynamics of the flow are sufficient to deduce the temperature at which any other streamline in the flow becomes saturated. The equation of state for vapour is then applied to deduce the saturation pressure for the water component of the atmospheric flow also. The first law of thermodynamics is then used to deduce the heat gain within a region due to precipitation from the flow. This heat loss is also used to obtain an estimate for the rate of hydrometeor fallout from this region of the flow.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"85 ","pages":"Article 104351"},"PeriodicalIF":1.8,"publicationDate":"2025-03-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143580002","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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