Asymptotic analysis of a micropolar fluid flow in a thin domain with a free and rough boundary

粗糙边界和非零边界条件对微极流体润滑过程的影响

Effects of rough boundary and nonzero boundary conditions on the lubrication process with micropolar fluid

本文研究微极流体在粗糙边界薄域中的润滑行为，施加非零微旋转边界条件并进行3D边值问题渐近分析，推导出简化数学模型，数值结果表明粗糙表面能增强线性滑块轴承的机械性能。

The p-Laplacian equation in a rough thin domain with terms concentrating on the boundary

In this work we use reiterated homogenization and unfolding operator approach to study the asymptotic behavior of the solutions of the $p$-Laplacian equation with Neumann boundary conditions set in a rough thin domain with concentrated terms on the boundary. We study weak, resonant and high roughness, respectively. In the three cases, we deduce the effective equation capturing the dependence on the geometry of the thin channel and the neighborhood where the concentrations take place.

粗糙度诱导的热微极流体在薄域中的流动效应

Roughness-induced effects on the thermomicropolar fluid flow through a thin domain

本文研究了粗糙边界薄通道中热微极流体流动的渐近行为，通过推导不同渐近模型揭示粗糙度对平均速度和微旋转的影响。

Nonlinear Reynolds equations for non-Newtonian thin-film fluid flows over a rough boundary

We consider a non-Newtonian fluid flow in a thin domain with thickness $η_\varepsilon$ and an oscillating top boundary of period $\varepsilon$. The flow is described by the 3D incompressible Navier-Stokes system with a nonlinear viscosity, being a power of the shear rate (power law) of flow index $p$, with $9/5\leq p<+\infty$. We consider the limit when the thickness tends to zero and we prove that the three characteristic regimes for Newtonian fluids are still valid for non-Newtonian fluids, i.e. Stokes roughness ($η_\varepsilon\approx \varepsilon$), Reynolds roughness ($η_\varepsilon\ll \var…

带粗糙边界的薄区域中Bingham流的渐近行为

Asymptotic behavior of a Bingham Flow in thin domains with rough boundary

该研究针对带粗糙边界的薄区域中不可压缩Bingham流问题，用适配线性展开算子分析小参数趋于零时的渐近行为，得到保持非线性的均匀化极限问题并给出非线性Darcy定律解释。

具有轻微粗糙边界的薄域内准牛顿流体流动的二维Carreau定律

Two-dimensional Carreau law for a quasi-newtonian fluid flow through a thin domain with a slightly rough boundary

针对薄域内具有Carreau定律粘度的稳态准牛顿Stokes流，考虑粗糙边界影响，通过渐近分析推导出有效非线性二维Reynolds模型，并利用先验估计和紧致性证明其合理性。

具有局部周期粗糙边界的薄通道中的p-Laplacian

The p-Laplacian in thin channels with locally periodic rough boundaries

本文研究具有局部周期粗糙边界的薄通道中p-Laplacian方程解的渐近行为，通过令参数趋于零建立极限模型。

Boundary Layer for a Non-Newtonian Flow over a Rough Surface

We analyze the effect of a rough surface on shear thinning and shear thickening fluids, modeled by power law stress tensors. The roughness is modeled by a small wavelength and small amplitude oscillation, parametrized by eps. We study the boundary layer corrector near the rough surface, and provide error estimates in terms of eps for the associated wall laws. With regards to previous studies, Mathematical difficulties arise from the nonlinearity of the corrector equations.

Local and global existence of solutions to a fourth-order parabolic equation modeling kinetic roughening and coarsening in thin films

In this paper we study both the Cauchy problem and the initial boundary value problem for the equation $\partial_tu+\mbox{div}\left(\nablaΔu-{\bf g}(\nabla u)\right)=0$. This equation has been proposed as a continuum model for kinetic roughening and coarsening in thin films. In the Cauchy problem, we obtain that local existence of a weak solution is guaranteed as long as the vector-valued function ${\bf g}$ is continuous and the initial datum $u_0$ lies in $C^1(\mathbb{R}^N)$ with $\nabla u_0(x)$ being uniformly continuous and bounded on $\mathbb{R}^N$ and that the global existence assertion a…

薄层流-热系统与固体本体域耦合的分析与模拟

Analysis and Simulation of a Fluid-Heat System in a Thin, Rough Layer in Contact With a Solid Bulk Domain

研究薄层与固体本体域间流-热耦合，考虑温度依赖粘度和对流热传输，分析非线性系统存在性、唯一性和能量估计，并通过多尺度收敛理论推导有效界面模型，通过数值模拟验证结果。

非等温多孔介质流动中表面粗糙度的影响

On the effects of surface roughness in non-isothermal porous medium flow

研究非等温Darcy-Brinkman薄液膜流动中周期性边界和粘性耗散的影响，通过渐近分析和周期展开方法，建立速度、压力和温度场收敛性，揭示粗糙度波长相对尺度耦合椭圆系统的主要贡献。

外延生长模型的粗糙噪声稳定化

Stabilization by rough noise for an epitaxial growth model

该研究针对外延生长模型，发现入射粒子波动产生的任意小时空白噪声可消除模型非线性相互作用，具备稳定动力学、抑制山丘生长的潜力。