We address a stability threshold problem of the Couette flow (y,0,0) in a uniform magnetic fleld alpha(sigma,0,1) with sigma is an element of Q for the 3D MHD equations on T & times;R & times;T. Previously, the authors in [27, 30] obtained the threshold gamma =1 for sigma is an element of R\Q satisfying a generic Diophantine condition, where they also proved gamma =4/3 for a general sigma is an element of R. In the present paper, we obtain the threshold gamma =1 in HN(N >13/2), hence improving the above results when sigma is a rational number. The nonlinear inviscid damping for velocity u(not equal)(2) is also established. Moreover, our result shows that the nonzero modes of a magnetic field has an amplification of order v-1/3 even on low regularity, which is very different from the case considered in [27, 30].

We address a threshold problem of the Couette flow (y, 0) in a uniform magnetic field (beta, 0) for the 2D MHD equation on T x R with fluid viscosity v and magnetic resistivity mu. The nonlinear enhanced dissipation and inviscid damping are also established. In particularly, when 0 < v <= (3) <= 1, we get a threshold v(1/2) mu 1/3 in H-N (N >= 4). When 0 < (3) <= v <= 1, we obtain a threshold min {v(1/2) mu (1/2) } min{1, v(-1) mu (1/3)}, hence improving the results in [19,14,22]. (c) 2026 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.

In this paper, we develop a stability threshold theorem for the 2D incompressible Navier-Stokes equations on the channel, supplemented with the no-slip boundary condition. The initial datum is close to the Couette flow in the following sense: the shear component of the perturbation is small, but independent of the viscosity ν. On the other hand, the x-dependent fluctuation is assumed small in a viscosity-dependent sense, namely, O(ν^1/2|log ν|^-2). Under this setup, we prove nonlinear enhanced dissipation of the vorticity and a time-integrated inviscid damping for the velocity. These stabilizing phenomena guarantee that the Navier-Stokes solution stays close to an evolving shear flow for all time. The analytical challenge stems from a time-dependent nonlocal term that appears in the associated linearized Navier-Stokes equations.

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In this work, we prove a threshold theorem for the 2D Navier-Stokes equations posed on the periodic channel, 𝕋× [-1,1] , supplemented with Navier boundary conditions ω |_y = ± 1 = 0 . Initial datum is taken to be a perturbation of Couette in the following sense: the shear component of the perturbation is assumed small (in an appropriate Sobolev space) but importantly is independent of ν . On the other hand, the nonzero modes are assumed size O(ν ^1/2) in an anisotropic Sobolev space. For such datum, we prove nonlinear enhanced dissipation and inviscid damping for the resulting solution. The principal innovation is to capture quantitatively the inviscid damping, for which we introduce a new Singular Integral Operator which is a physical space analogue of the usual Fourier multipliers which are used to prove damping. We then include this SIO in the context of a nonlinear hypocoercivity framework.

In this article, we study the regularity theory for two linear equations that are important in fluid dynamics: the passive scalar equation for (time-varying) shear flows close to Couette in T x [-1, 1] with vanishing diffusivity v-* 0 and the Poisson equation with right-hand side behaving in similar function spaces to such a passive scalar. The primary motivation for this work is to develop some of the main technical tools required for our treatment of the (nonlinear) 2D NavierStokes equations, carried out in our companion work. Both equations are studied with homogeneous Dirichlet conditions (the analogue of a Navier slip-type boundary condition) and the initial condition is taken to be compactly supported away from the walls. We develop smoothing estimates with the following three features: (1) Uniform-in-v regularity is with respect to 8x and a time-dependent adapted vector-field Gamma which approximately commutes with the passive scalar equation (as opposed to 'flat' derivatives), and a scaled gradient /vV; (2) (partial derivative x, f)-regularity estimates are performed in Gevrey spaces with regularity that depends on the spatial coordinate, y (what we refer to as 'pseudo-Gevrey'); (3) The regularity of these pseudo-Gevrey spaces degenerates to finite regularity near the center of the channel and hence standard Gevrey product rules and other amenable properties do not hold. Nonlinear analysis in such a delicate functional setting is one of the key ingredients to our companion paper, [5], which proves the full nonlinear asymptotic stability of the Couette flow with slip boundary conditions. The present article introduces new estimates for the associated linear problems in these degenerate pseudo-Gevrey spaces, which is of independent interest. of independent interest. @ 2025 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).

The wave glider is an unmanned surface vehicle propelled by wave energy, consisting of three main components: a surface float, a submarine glider, and a tether. The submarine glider serves as the primary propulsion mechanism, converting the wave-induced motions of the float into forward thrust, which is crucial for the wave glider’s energy absorption efficiency. However, predicting the motion performance of the submarine glider presents a significant challenge due to its complex and unique structure. In this study, we establish a kinematic and dynamic model of the submarine glider’s hydrofoils, considering the elastic effects such as spring stiffness, spring preload, and spring attachment positions. To support this model, wind tunnel tests were conducted to determine the lift and drag coefficients of the submarine glider under various motion states. Utilizing the elastic hydrofoil model and the experimentally obtained lift and drag coefficients, we developed a comprehensive kinematic and dynamic simulation model of the submarine glider under heave excitation forces. To validate the accuracy of this model, performance tests for the submarine glider were designed under different vertical excitation forces , with results compared to simulation outcomes. The findings indicate that the deviation between simulated and experimental outcomes is less than 5%, demonstrating the model’s precision. This accurate simulation capability allows for detailed analysis of the effects of various design parameters on the glider’s performance and lays a solid foundation for high-accuracy motion simulation of the entire wave glider.

For the water-air system, the bulk density ratio is as high as about 1000; no model can fully tackle such a high density ratio system. In the Navier-Stokes and Euler equations, the density ρ within the water-air interface is assumed to be a constant based on the Boussinesq approximation namely ρ(d𝐮/d t), which does not account for the true momentum evolution d (ρ𝐮)/d t (𝐮-fluid velocity). Here, we present an alternative theory for the density evolution equations of immiscible fluids in computational fluid dynamics, differing from the concept of Navier-Stokes and Euler equations. Our derivation is built upon the physical principle of energy minimization from the aspect of thermodynamics. The present results provide a generalization of Bernoulli's principle for energy conservation and a general formulation for the sound speed. The present model can be applied for immiscible fluids with arbitrarily high density ratios, thereby, opening a new window for computational fluid dynamics both for compressible and incompressible fluids.

The upstream self-diffusion of dissociated protons induces long-lasting electricity generation in 2D nanochannels of MXene/PVA film with low water permeability.

We give a novel vorticity formulation for the 3D Navier-Stokes equations with Dirichlet boundary conditions. Via a resolvent argument, we obtain Green's function and establish an upper bound, which is the 3D analog of [24]. Moreover, we prove similar results for the corresponding Stokes problem with more general mixed boundary conditions.

We address the local well-posedness for the stochastic Navier–Stokes system with multiplicative cylindrical noise in the whole space. More specifically, we prove that there exists a unique local strong solution to the system in L^p(ℝ^3) for p>3 .

We consider a general class of non-diffusive active scalar equations with constitutive laws obtained via an operator $\mathbf{T}$ that is singular of order $r_0\in[0,2]$. For $r_0\in(0,1]$ we prove well-posedness in Gevrey spaces $G^s$ with $s\in[1,\frac{1}{r_0})$, while for $r_0\in[1,2]$ and further conditions on $\mathbf{T}$ we prove ill-posedness in $G^s$ for suitable $s$. We then apply the ill/well-posedness results to several specific non-diffusive active scalar equations including the magnetogeostrophic equation, the incompressible porous media equation and the singular incompressible porous media equation.

We consider the 2D, incompressible Navier-Stokes equations near the Couette flow, ω^(NS) = 1 + ϵω, set on the channel 𝕋× [-1, 1], supplemented with Navier boundary conditions on the perturbation, ω|_y = ± 1 = 0. We are simultaneously interested in two asymptotic regimes that are classical in hydrodynamic stability: the long time, t →∞, stability of background shear flows, and the inviscid limit, ν→ 0 in the presence of boundaries. Given small (ϵ≪ 1, but independent of ν) Gevrey 2- datum, ω_0^(ν)(x, y), that is supported away from the boundaries y = ± 1, we prove the following results: ω^(ν)(t) - 1/2π∫ω^(ν)(t) dx _L^2≲ϵ e^-δν^1/3 t, (Enhanced Dissipation) ⟨ t ⟩u_1^(ν)(t) - 1/2π∫ u_1^(ν)(t) dx_L^2 + ⟨ t ⟩^2 u_2^(ν)(t)_L^2≲ϵ e^-δν^1/3 t, (Inviscid Damping) ω^(ν) - ω^(0)_L^∞≲ϵν t^3+η, t ≲ν^-1/(3+η) (Long-time Inviscid Limit) This is the first nonlinear asymptotic stability result of its type, which combines three important physical phenomena at the nonlinear level: inviscid damping, enhanced dissipation, and long-time inviscid limit in the presence of boundaries. The techniques we develop represent a major departure from prior works on nonlinear inviscid damping as physical space techniques necessarily play a central role. In this paper, we focus on the primary nonlinear result, while tools for handling the linearized parabolic and elliptic equations are developed in our separate, companion work.

To study the flow field and hydrodynamic characteristics of hyperbolic flow around a cylinder caused by an internal solitary wave, the hyperbolic flow around the cylinder induced by the inner solitary wave, inlet condition is the lower deep horizontal velocity induced by the inner solitary wave and the two-dimensional Navier-Stokes equation is used as the flow field control equation according to the applicability conditions of the eKdV inner solitary wave theory. A numerical simulation method for the nonlinear action of internal solitary wave-induced hyperbolic flow on a horizontal cylinder is established. A series of calculation results show that the numerical simulation results of horizontal force on the cylinder are in good agreement with experimental results. The wakefield of hyperbolic flow around a cylinder has distinct characteristics. In the process of flow around the cylinder, the vortex does not fall off alternately and the lateral lift force is neglected. The force of internal solitary wave-induced hyperbolic flow on the cylinder is non-centrosymmetric, and with the increase of maximum Reynolds number and characteristic period, the horizontal resistance of the cylinder becomes unidirectional. Therefore, the maximum Reynolds number and the characteristic period affect the horizontal force of internal solitary wave-induced hyperbolic flow on a two-dimensional cylinder.

Abstract This paper concerns the existence of global weak solutions á la Leray for compressible Navier–Stokes–Fourier systems with periodic boundary conditions and the truncated virial pressure law which is assumed to be thermodynamically unstable. More precisely, the main novelty is that the pressure law is not assumed to be monotone with respect to the density. This provides the first global weak solutions result for the compressible Navier-Stokes-Fourier system with such kind of pressure law which is strongly used as a generalization of the perfect gas law. The paper is based on a new construction of approximate solutions through an iterative scheme and fixed point procedure which could be very helpful to design efficient numerical schemes. Note that our method involves the recent paper by the authors published in Nonlinearity (2021) for the compactness of the density when the temperature is given.

divu = 0 (1.2) u|t=0 = u0 (1.3) on the half-space domain H = T × R+ = {(x, y) ∈ T × R : y ≥ 0}, with the periodic boundary condition in x, and the no-slip boundary condition u|y=0 = 0. (1.4) Here we take the torus T = [−π, π], but our results apply for any torus T = [−a, a] for a > 0. The goal of this paper is to study the growth mechanism of the boundary layers in the inviscid limit problem of the Navier-Stokes system for initial data that are analytic only near the boundary of the domain, and are Sobolev smooth away from the boundary. As an easy implication, we know this growing procedure is still valid for analytic initial data or Sobolev initial data with support away from the boundary, which are considered in [SC98a, SC98b], and [Mae14] respectively.

We establish the validity of the Euler $$+$$ Prandtl approximation for solutions of the Navier-Stokes equations in the half plane with the Dirichlet boundary conditions, in the vanishing viscosity limit, for initial data which are analytic only near the boundary, and Sobolev smooth away from the boundary. Our proof does not require higher order correctors, and works directly by estimating an $$L^{1}$$ -type norm for the vorticity of the error term in the expansion Navier-Stokes $$-($$ Euler $$+$$ Prandtl). An important ingredient in the proof is the propagation of local analyticity for the Euler equation, a result of independent interest

This paper concerns the existence of global weak solutions a la Leray for compressible Navier-Stokes equations with a pressure law which depends on the density and on time and space variables t and x. The assumptions on the pressure contain only locally Lipschitz assumption with respect to the density variable and some hypothesis with respect to the extra time and space variables. It may be seen as a first step to consider heat-conducting Navier-Stokes equations with physical laws such as the truncated virial assumption. The paper focuses on the construction of approximate solutions through a new regularized and fixed point procedure and on the weak stability process taking advantage of the new method introduced by the two first authors with a careful study of an appropriate regularized quantity linked to the pressure.

OBJECTIVE:Tension band plating has recently gained widespread acceptance as a method of correcting angular limb deformities in skeletally immature patients. We examined the role of biomechanics in procedural failure and devised a new method of reducing the rate of implant failure.METHODS:In the biomechanical model, afterload (static or cyclic) was applied to each specimen. The residual stress of the screw combined with different screw sizes and configurations were measured and compared by X-ray diffraction. With regard to static load and similar conditions, the stress distribution was analyzed according to a three-dimensional finite element model.RESULTS:The residual stress was close to zero in the static tension group, whereas it was very high in the cyclic load group. The residual stress of screws was significantly lower in the convergent group and parallel group than in the divergent group. The finite element model showed similar results.CONCLUSIONS:In both the finite element analysis and biomechanical tests, the maximum stress of the screw was concentrated at the position where the screws enter the cortex. Cyclic loading is the primary cause of implant failure.

为解决风洞实验室模型风载荷实验测量相关技术问题,开发了实验测量系统并展开实验研究;根据该类型实验特点及要求,设计了测量系统方案,组建测量软硬件系统,采用多种传感器完整测量风载荷、风速、温湿度等多种数据,进行数据融合处理得到风载荷系数;为确保实验测量精度,考虑了天平零漂、空气密度变化、模型自重干扰等因素的影响,通过分析给出了其各自的数据处理方法以得到有效的风载荷;在此基础上完成测量程序/共享软件的编写,基本实现了实验测量自动化,避免手工介入,实验效率大幅提高;最后应用本文结果展开实际实验测量,定量分析各因素对于测量结果的影响,结果表明,空气密度变化、模型自重干扰、风速波动对模型风载荷结果影响较为明显,在计算风载荷系数时需采用每一工况的实时数据;而信号噪声对均值结果几乎无影响而不用考虑。