相关论文: Higher-order boundary layers and regularity for St…
In the present work, we propose to extend to the Stokes problem a fictitious domain approach inspired by eXtended Finite Element Method and studied for Poisson problem in [Renard]. The method allows computations in domains whose boundaries…
We develop numerical methods to simulate the fluid-mechanical erosion of many bodies in two-dimensional Stokes flow. The broad aim is to simulate the erosion of a porous medium (e.g. groundwater flow) with grain-scale resolution. Our fluid…
Processing the data from a large variety of zero-pressure-gradient boundary layer flows shows that the Reynolds-number-dependent scaling law, which the present authors obtained earlier for pipes, gives an accurate description of the…
In this paper, we propose a high-order extension of the multiscale method introduced by the authors in [SIAM J. Numer. Anal., 63(4) (2025), pp. 1617--1641] for heterogeneous Stokes problems, while also providing several other improvements,…
We investigate a class of free boundary problems with oscillatory singularities within stochastic materials. Our main result yields sharp regularity estimates along the free boundary, provided the power of the singularity varies in a…
In this paper, we derive sharp bounds on the semigroup of the linearized incompressible Navier-Stokes equations near a stationary shear layer in the half plane and in the half space ($\mathbb{R}_+^2$ or $\mathbb{R}_+^3$), with Dirichlet…
We study the phenomenon of spatiotemporal stochastic resonance (STSR) in a chain of diffusively coupled bistable oscillators. In particular, we examine the situation in which the \textit{global} STSR response is controlled by a…
A framework is developed for a robust and highly accurate numerical solution of the coupled Stokes-Darcy system in three dimensions. The domain decomposition method is based on a Dirichlet-Neumann type splitting of the interface conditions…
In the well-known book of Lions [{\em Mathematical topics in fluid mechanics. Incompressible models}, 1996], global existence results of finite energy weak solutions of the inhomogeneous incompressible Navier-Stokes equations (INS) were…
For a general class of hyperbolic-parabolic systems including the compressible Navier-Stokes and compressible MHD equations, we prove existence and stability of noncharacteristic viscous boundary layers for a variety of boundary conditions…
We study the boundary behaviour of solutions to second order parabolic linear equations in moving domains. Our main result is a higher order boundary Harnack inequality in $C^1$ and $C^{k,\alpha}$ domains, providing that the quotient of two…
We provide an unconditional $L^2$ upper bound for the boundary layer separation of Leray-Hopf solutions in a smooth bounded domain. By layer separation, we mean the discrepancy between a (turbulent) low-viscosity Leray-Hopf solution $u^\nu$…
The eigenvalues and eigenfunctions of the Stokes operator have been the subject of intense analytical investigation and have applications in the study and simulation of the Navier-Stokes equations. As the Stokes operator is a fourth-order…
This paper is concerned with the homogenization of Dirichlet problem of elliptic systems in a bounded, smooth domain of finite type. Both the coefficients of the elliptic operator and the Dirichlet boundary data are assumed to be periodic…
We consider the steady Stokes equations in a bounded domain with forcing in divergence form supplemented with no-slip boundary conditions. We provide a maximal regularity theory in Campanato spaces (inlcuding $\mathrm{BMO}$ and…
The stability and transition in the bottom boundary layer under a solitary wave are analysed in the presence of finite amplitude disturbances. First, the receptivity of the boundary layer is investigated using a linear input-output…
In \cite{X-Z DCS1}, we introduced discrete conformal structures on surfaces with boundary via an axiomatic framework, and provided a classification of such discrete conformal structures. The present work focuses on the rigidity and…
Semi-linear elliptic boundary problems with non-linearities of product type are considered, in particular the stationary Navier--Stokes equations. Regularity and existence results are dealt with in the Besov and Triebel--Lizorkin spaces,…
We show that finite-energy weak solutions to the incompressible Navier--Stokes equations on a three-dimensional bounded smooth domain are regular up to the boundary, provided that the $L^4_tL^4_x$-norm of the solution is smaller than a…
We study numerically transitional coherent structures in a boundary-layer flow with homogeneous suction at the wall (the so-called asymptotic suction boundary layer ASBL). The dynamics restricted to the laminar-turbulent separatrix is…