相关论文: Boundary Layer of Transport Equation with In-Flow …

The linear growth of operators in local quantum systems leads to an effective lightcone even if the system is non-relativistic. We show that consistency of diffusive transport with this lightcone places an upper bound on the diffusivity: $D…

In this article we establish linear inviscid damping with optimal decay rates around 2D Taylor-Couette flow and similar monotone flows in an annular domain $B_{r_{2}}(0) \setminus B_{r_{1}}(0) \subset \mathbb{R}^{2}$. Following recent…

In this paper we provide a variational characterisation for a class of non-linear evolution equations with constant non-negative Dirichlet boundary conditions on a bounded domain as gradient flows in the space of non-negative measures. The…

We consider the stability of two-dimensional viscous flows in an annulus with permeable boundary. In the basic flow, the velocity has nonzero azimuthal and radial components, and the direction of the radial flow can be from the inner…

In this paper, we establish the mathematical validity of the Prandtl boundary layer theory for a class of nonlinear plane parallel flow of nonhomogeneous incompressible Navier-Stokes equations. The convergence for the density and velocity…

This investigation deals with the analysis of stagnation point heat transfer and corresponding flow features of hydromagnetic viscous incompressible fluid over a vertical shrinking sheet. The considered sheet is assumed to be permeable and…

Nonlinear convection, the source of turbulence in fluid flows, may hold the key to stabilizing turbulence by solving a specific cubic polynomial equation. We consider the incompressible Navier-Stokes equations in a two-dimensional channel.…

We study the asymptotic diffusion processes with (generally nonlocal) open boundaries in one dimension which are exactly solvable by means of the recently developed recursion formula. We investigate the stationary states, which cannot be…

A finite difference method is constructed to solve singularly perturbed convection-diffusion problems posed on smooth domains. Constraints are imposed on the data so that only regular exponential boundary layers appear in the solution. A…

A system of boundary-domain integral equations is derived from the bidimensional Dirichlet problem for the diffusion equation with variable coefficient using the novel parametrix from [22] different from the one in [5,18]. Mapping…

We consider the inverse problem of determining different type of information about a diffusion process, described by ordinary or fractional diffusion equations stated on a bounded domain, like the density of the medium or the velocity field…

In this paper, we validate the boundary layer theory for 2D steady viscous incompressible magnetohydrodynamics (MHD) equations in a domain $\{(X, Y)\in[0, L]\times\mathbb{R}_+\}$ under the assumption of a moving boundary at $\{Y=0\}$. The…

We prove the existence and uniqueness of maximal solutions to the 3D SALT (Stochastic Advection by Lie Transport, [Holm arXiv:1410.8311]) Navier-Stokes Equation in velocity and vorticity form, on the torus and the bounded domain…

A discrete drift-diffusion model is derived from a microscopic sequential tunneling model of charge transport in weakly coupled superlattices provided temperatures are low or high enough. Realistic transport coefficients and novel contact…

Due to computational complexity, fluid flow problems are mostly defined on a bounded domain. Hence, capturing fluid outflow calls for imposing an appropriate condition on the boundary where the said outflow is prescribed. Usually, the…

We consider variational inequality solutions with prescribed gradient constraints for first order linear boundary value problems. For operators with coefficients only in $L^2$, we show the existence and uniqueness of the solution by using a…

This paper deals with collisionless transport equations in bounded open domains $\Omega \subset \R^{d}$ $(d\geq 2)$ with $\mathcal{C}^{1}$ boundary $\partial \Omega $, orthogonally invariant velocity measure $\bm{m}(\d v)$ with support…

A new definition of conditional invariance for boundary value problems involving a wide range of boundary conditions (including initial value problems as a special case) is proposed. It is shown that other definitions worked out in order to…

The solution of partial differential equations (PDEs) on complex domains often presents a significant computational challenge by requiring the generation of fitted meshes. The Diffuse Domain Method (DDM) is an alternative which reformulates…

We consider a coupled model for fluid flow and transport in a domain consisting of two bulk regions separated by a thin porous layer. The thickness of the layer is of order $\varepsilon$ and the microscopic structure of the layer is…