Journal of Mathematical Fluid Mechanics最新文献

{"title":"Uniform Stability and the Optimal Time decay of Strong Solutions to the Incompressible Kinetic-Magnetohydrodynamic System Arising in Magnetized Plasmas","authors":"Fucai Li,&nbsp;Jinkai Ni,&nbsp;Man Wu","doi":"10.1007/s00021-026-01050-5","DOIUrl":"10.1007/s00021-026-01050-5","url":null,"abstract":"<div><p>In this paper, we investigate the uniform stability and optimal time decay of strong solutions to the incompressible kinetic-magnetohydrodynamic (kinetic-MHD) system in the whole space <span>(mathbb {R}^3)</span>. This model consists of a kinetic equation describing the evolution of energetic particles and the incompressible MHD equations governing the dynamics of the fluid and magnetic field, coupled through Lorentz forces. Under the assumption that the initial data are small perturbations near the spatially homogeneous equilibrium (<i>M</i>, 0, 0), we first establish the global existence of strong solutions in the <span>(L_v^2(H_x^2)times H_x^2times H_x^2)</span> framework, without imposing any regularity assumption on the velocity derivatives of the kinetic perturbation <i>f</i>. Under an additional smallness assumption in <span>(L^1)</span>, by employing the low-high frequency decomposition method and the time-weighted energy method, we address the difficulties arising from the velocity-weighted term and the loss of velocity derivatives in <span>(vtimes Bcdot nabla _v f)</span>. As a result, we obtain the optimal time decay rates of all spatial derivatives up to order two, including the highest-order rate <span>((1+t)^{-7/4})</span>. Here, <span>(a=int _{mathbb {R}^3}sqrt{M}f,textrm{d}v)</span> and <span>(b=int _{mathbb {R}^3}vsqrt{M}f,textrm{d}v)</span> denote the zeroth and first velocity moments of <i>f</i>, respectively. We further identify a magnetic-field-induced dissipation mechanism such that <i>b</i> and <span>(nabla b)</span> decay one-half order faster than the corresponding orders of the full solution, while accelerated decay also holds for <span>(partial _t a)</span> and <span>(partial _t b)</span>. Furthermore, a refined difference-energy method yields the uniform stability of strong solutions. In the periodic domain <span>(mathbb {T}^3)</span>, we show that <i>f</i> and <i>B</i> decay exponentially, whereas the fluid velocity <i>u</i> remains uniformly bounded, which differs from kinetic-fluid systems with drag-force coupling. To the best of our knowledge, this is the first result concerning the uniform stability and optimal time decay of strong solutions for this kinetic-MHD model.</p></div>","PeriodicalId":649,"journal":{"name":"Journal of Mathematical Fluid Mechanics","volume":"28 4","pages":""},"PeriodicalIF":1.5,"publicationDate":"2026-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148926688","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}

{"title":"On Stability of Gravity Driven Quantum Magnetized Plasmas with Magnetic Damping","authors":"Xuyan Zhang,&nbsp;Xiaole Zheng","doi":"10.1007/s00021-026-01053-2","DOIUrl":"10.1007/s00021-026-01053-2","url":null,"abstract":"<div><p>This work provides a rigorous mathematical investigation into the inhibition of the Rayleigh–Taylor (RT) instability by quantum effects within a magnetized plasma. We prove such inhibition phenomenon for an incompressible quantum magnetohydrodynamic (QMHD) model that incorporates a magnetic damping term <span>(nu B)</span> with Navier (slip) boundary condition in a <span>(3textrm{D})</span> horizontal slab domain. More precisely, we establish the existence of a critical threshold <span>(varepsilon _c)</span> for the quantum parameter <span>(varepsilon =hbar ^2/4 m_e m_i)</span>, which scales the Bohm potential <span>(2rho nabla left( frac{{Delta sqrt{rho }}}{{sqrt{rho }}}right) )</span>, and find when <span>(varepsilon &gt;varepsilon _c)</span>, small perturbations around an RT-unstable equilibrium decay algebraically in time, demonstrating nonlinear stability. This delineates a sharp stability criterion, confirming that the quantum potential can suppress the RT instability, but only when its strength surpasses a precisely defined critical value.</p></div>","PeriodicalId":649,"journal":{"name":"Journal of Mathematical Fluid Mechanics","volume":"28 4","pages":""},"PeriodicalIF":1.5,"publicationDate":"2026-08-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148837486","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}

{"title":"Inhomogeneous 2D Navier–Stokes Equations: Existence, Uniqueness, Stability, Continuity in Time and Energy Conservation of Weak Solutions","authors":"Stefan Škondrić","doi":"10.1007/s00021-026-01052-3","DOIUrl":"10.1007/s00021-026-01052-3","url":null,"abstract":"<div><p>We present a novel and direct proof of the existence and uniqueness of weak solutions of the inhomogeneous incompressible Navier–Stokes equations without vacuum. The analysis we employ to prove the strong convergence of the approximating sequence, which is based on the relative energy method, reveals how to conclude the stability and uniqueness of weak solutions. To the best of our knowledge, these global-in-time stability estimates are completely new. Furthermore, for the first time, we establish energy conservation for weak solutions.</p></div>","PeriodicalId":649,"journal":{"name":"Journal of Mathematical Fluid Mechanics","volume":"28 4","pages":""},"PeriodicalIF":1.5,"publicationDate":"2026-08-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00021-026-01052-3.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148782558","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}

{"title":"On an Initial Value Problem Describing the Small Oscillations of a Floating Cylinder","authors":"Vicente Ocqueteau,&nbsp;Marius Tucsnak","doi":"10.1007/s00021-026-01047-0","DOIUrl":"10.1007/s00021-026-01047-0","url":null,"abstract":"<div><p>We study a coupled PDE-ODE system modeling the small oscillations of a floating cylinder interacting with small water waves. We consider the case when the floating body is an infinite circular cylinder, so that the equations of the free surface of the fluid can be written in one space dimension. The governing equations are formulated as an abstract evolution equation in a suitable Hilbert space, and we establish the well-posedness of the associated initial value problem. A key element of the proof is the analysis of a partial Dirichlet-to-Neumann map on an unbounded domain with a non-smooth boundary.</p></div>","PeriodicalId":649,"journal":{"name":"Journal of Mathematical Fluid Mechanics","volume":"28 4","pages":""},"PeriodicalIF":1.5,"publicationDate":"2026-08-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148751438","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}

{"title":"Refined Liouville-Type Theorems for the 3D Stationary Navier–Stokes Equations via Head Pressure Estimates","authors":"Changzhi Liu,&nbsp;Wenke Tan","doi":"10.1007/s00021-026-01049-y","DOIUrl":"10.1007/s00021-026-01049-y","url":null,"abstract":"<div><p>Based on the work of Chae [4], we establish two refined Liouville-type theorems for the three-dimensional stationary Navier–Stokes equations. The main idea of this paper is to construct divergent series via the summation of integrals over mutually disjoint level-set shells, which leads to contradictions with the finite Dirichlet energy of velocity and the finite <span>(L^{frac{3}{2}})</span> norm of the gradient of the total head pressure, respectively. This approach allows for a logarithmic growth factor to be included in the polynomial decay requirements previously prescribed in Chae’s work [4].</p></div>","PeriodicalId":649,"journal":{"name":"Journal of Mathematical Fluid Mechanics","volume":"28 4","pages":""},"PeriodicalIF":1.5,"publicationDate":"2026-08-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148751437","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}

{"title":"Global Decay of Perturbations of Equilibrium States for One-Dimensional Heat Conducting Compressible Fluids of Korteweg Type","authors":"Ramón G. Plaza,&nbsp;José M. Valdovinos","doi":"10.1007/s00021-026-01046-1","DOIUrl":"10.1007/s00021-026-01046-1","url":null,"abstract":"<div><p>This paper studies the one dimensional Navier-Stokes-Fourier-Korteweg system of equations describing the evolution of a heat-conducting compressible fluid that exhibits viscosity and capillarity. The main goal of the present analysis is to examine the dissipative structure of the system and to prove the global existence and the asymptotic decay of perturbations of equilibrium states. For that purpose, a novel nonlinear change of perturbed state variables, which takes into account that the conserved quantities contain density gradients, is introduced. These new perturbation variables satisfy a partially symmetric system whose linearization fulfills the generalized genuine coupling condition of Humpherys [41] for higher order systems. It is shown that the linearized system is symbol symmetrizable and an appropriate compensating matrix is constructed. This procedure allows to obtain linear decay rates which underlie a dissipative mechanism of regularity-gain type. This linear dissipative structure implies, in turn, the global decay of small perturbations to constant equilibrium states as solutions to the full nonlinear system.</p></div>","PeriodicalId":649,"journal":{"name":"Journal of Mathematical Fluid Mechanics","volume":"28 4","pages":""},"PeriodicalIF":1.5,"publicationDate":"2026-08-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00021-026-01046-1.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148652347","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}

{"title":"Large Time Decay of the Oseen Flow in Exterior Domains Subject to the Navier Slip-with-Friction Boundary Condition","authors":"Toshiaki Hishida","doi":"10.1007/s00021-026-01039-0","DOIUrl":"10.1007/s00021-026-01039-0","url":null,"abstract":"<div><p>Consider the motion of a viscous incompressible fluid filling a 3D exterior domain <span>(Omega )</span> subject to the Navier slip-with-friction boundary condition as well as outflow at infinity. For the Oseen system as the linearization, we discuss the resolvent set under a certain relationship among the geometry of the boundary <span>(partial Omega )</span>, friction coefficient <span>(alpha (x))</span> and the outflow <span>(u_infty )</span>. We then study the regularity of the resolvent near the origin in the complex plane to develop <span>(L^q)</span>-<span>(L^r)</span> decay estimates of the Oseen semigroup provided that <span>(alpha (x)+u_infty cdot nu (x)/2ge 0)</span> for every <span>(xin partial Omega )</span>, where <span>(nu (x))</span> stands for the outward unit normal to the boundary <span>(partial Omega )</span>.</p></div>","PeriodicalId":649,"journal":{"name":"Journal of Mathematical Fluid Mechanics","volume":"28 3","pages":""},"PeriodicalIF":1.5,"publicationDate":"2026-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00021-026-01039-0.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148614116","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}

{"title":"Continuous Data Assimilation For 2D Stochastic Navier–Stokes Equations","authors":"Hakima Bessaih,&nbsp;Benedetta Ferrario,&nbsp;Oussama Landoulsi,&nbsp;Margherita Zanella","doi":"10.1007/s00021-026-01043-4","DOIUrl":"10.1007/s00021-026-01043-4","url":null,"abstract":"<div><p>Continuous data assimilation methods, such as the nudging algorithm introduced by Azouani, Olson, and Titi (AOT) [2], are known to be highly effective in deterministic settings for asymptotically synchronizing approximate solutions with observed dynamics. In this work, we extend this framework to a stochastic regime by considering the two-dimensional incompressible Navier-Stokes equations subject to either additive or multiplicative noise. We establish sufficient conditions on the nudging parameter and the spatial observation scale that guarantee convergence of the nudged solution to the true stochastic flow. In the case of multiplicative noise, convergence holds in expectation, with exponential or polynomial rates depending on the growth of the noise covariance. For additive noise, we obtain the exponential convergence both in expectation and pathwise. These results yield a stochastic generalization of the AOT theory, demonstrating how the interplay between random forcing, viscous dissipation and feedback control governs synchronization in stochastic fluid systems.</p></div>","PeriodicalId":649,"journal":{"name":"Journal of Mathematical Fluid Mechanics","volume":"28 3","pages":""},"PeriodicalIF":1.5,"publicationDate":"2026-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00021-026-01043-4.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148613987","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}

{"title":"Existence of Global Weak Solutions to a Parabolic p-Laplacian Problem with Convective Term","authors":"Angelica Pia Di Feola,&nbsp;Michael Růžička","doi":"10.1007/s00021-026-01042-5","DOIUrl":"10.1007/s00021-026-01042-5","url":null,"abstract":"<div><p>For a given bounded domain <span>(Omega subset mathbb R^3)</span>, with <span>(C^2)</span> boundary, and a given instant of time <span>(T&gt;0)</span>, we prove the existence of a global weak solution on (0, <i>T</i>), which satisfies a maximum principle, to a parabolic <i>p</i>-Laplacian system with convective term without divergence constraint for any <span>(pin (1,2))</span> and the initial datum in <span>(L^infty (Omega ))</span>. Moreover, we study the finite-time extinction property for suitable initial data.</p></div>","PeriodicalId":649,"journal":{"name":"Journal of Mathematical Fluid Mechanics","volume":"28 3","pages":""},"PeriodicalIF":1.5,"publicationDate":"2026-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00021-026-01042-5.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148613986","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}

{"title":"Initial-Boundary Value Problems for the 2D MHD Equations with Partial Dissipation","authors":"Quansen Jiu,&nbsp;Xiaoxiao Suo","doi":"10.1007/s00021-026-01045-2","DOIUrl":"10.1007/s00021-026-01045-2","url":null,"abstract":"<div><p>This paper studies the initial boundary value problems for the 2D MHD equations with vertical dissipation and horizontal magneto damping in a strip domain. The proof is nontrivial and relies on a sophisticated analytical framework involving anisotropic norms, time-derivative estimates, and time-weighted energy functionals. To address the challenges posed by weak dissipation and boundary effects, we develop a set of anisotropic inequalities and establish key auxiliary estimates. For sufficiently small initial data, a careful analysis of the nonlinear terms then leads to the global well-posedness of the system in the Sobolev setting <span>(H^3)</span>. Furthermore, the <span>(H^{2})</span>-norm of the velocity field and the magnetic field are shown to decay exponentially in time.</p></div>","PeriodicalId":649,"journal":{"name":"Journal of Mathematical Fluid Mechanics","volume":"28 3","pages":""},"PeriodicalIF":1.5,"publicationDate":"2026-07-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148613863","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}