Related papers: Estimates for stress concentration between two adj…
We consider an insulated conductivity model with two neighboring inclusions of $m$-convex shapes in $\mathbb{R}^{d}$ when $m\geq2$ and $d\geq3$. We establish the pointwise gradient estimates for the insulated conductivity problem and…
We derive the explicit Poisson kernel of Stokes equations in the half space with nonhomogeneous Navier boundary condition (BC) for both infinite and finite slip length. By using this kernel, for any $q>1$, we construct a finite energy…
Consider the diffusive Hamilton-Jacobi equation $$u_t-\Delta u=|\nabla u|^p+h(x)\ \ \text{ in } \Omega\times(0,T)$$ with Dirichlet conditions, which arises in stochastic control problems as well as in KPZ type models. We study the question…
We study the insulated conductivity problem with inclusions embedded in a bounded domain in $\mathbb{R}^n$. The gradient of solutions may blow up as $\varepsilon$, the distance between inclusions, approaches to $0$. An upper bound for the…
A numerical validation of the stress-jump coupling conditions for Stokes-Darcy flow in two dimensions is presented, addressing a gap that has remained since their introduction by Angot et al.. These conditions, formulated for arbitrary flow…
We study a fully discrete finite element approximation of a model for unsteady flows of rate-type viscoelastic fluids with stress diffusion in two and three dimensions. The model consists of the incompressible Navier--Stokes equation for…
We consider extensional flows of a dense layer of spheres in a viscous fluid and employ force and torque balances to determine the trajectory of particle pairs that contribute to the stress. In doing this, we use Stokesian dynamics…
We are concerned with the field concentration between two nearly-touching inclusions with high-contrast material parameters, which is a central topic in the theory of composite materials. The degree of concentration is characterised by the…
This paper is concerned with the stress concentration phenomenon in elastic composite materials when the inclusions are very closely spaced. We investigate the gradient blow-up estimates for the Lam\'{e} system of linear elasticity with…
We consider the system of partial differential equations governing two-dimensional flows of a robust class of viscoelastic rate-type fluids with stress diffusion, involving a general objective derivative. The studied system generalizes the…
In this paper, we construct a simple and robust two-point finite volume discretization applicable to isotropic linearized elasticity, valid in also in the incompressible Stokes' limit. The discretization is based only on co-located,…
The paper addresses stability and finite element analysis of the stationary two-phase Stokes problem with a piecewise constant viscosity coefficient experiencing a jump across the interface between two fluid phases. We first prove a priori…
A convenient approach to derive simple expressions for properties of Stokes flows with low levels of slip is presented. The method is based on a series expansion of a Stokes-flow solution (one satisfying a Navier slip boundary condition)…
We study the insulated conductivity problem with inclusions embedded in a bounded domain in $\mathbb{R}^n$. The gradient of solutions may blow up as $\varepsilon$, the distance between inclusions, approaches to $0$. It was known that the…
Although the numerical results suggest the optimal convergence order of the two-grid finite element decoupled scheme for mixed Stokes-Darcy model with Beaver-Joseph-Saffman interface condition in literatures, the numerical analysis only get…
Fluid and solute transfer in X-junctions between straight channels is shown to depend critically on the junction angle in the Stokes flow regime. Experimentally, water and a water-dye solution are injected at equal flow rates in two facing…
We study the insulated conductivity problem with inclusions embedded in a bounded domain in $\mathbb{R}^n$. It was known that in the setting of strictly convex inclusions, the gradient of solutions may blow up as the distance between…
In this paper, we obtain a blow up criterion for strong solutions to the 3-D compressible Naveri-Stokes equations just in terms of the gradient of the velocity, similar to the Beal-Kato-Majda criterion for the ideal incompressible flow. The…
Stokes flows are a type of fluid flow where convective forces are small in comparison with viscous forces, and momentum transport is entirely due to viscous diffusion. Besides being routinely used as benchmark test cases in numerical fluid…
Analytical method for the second-order homogenization of two-phase composites within Mindlin-Toupin strain gradient elasticity theory is proposed. Direct approach and self-consistent approximation are used to reduce the homogenization…