Related papers: Green function for linearized Navier-Stokes around…
In this paper we will show several properties of the Green's functions related to various boundary value problems of arbitrary even order. In particular, we will write the expression of the Green's functions related to the general…
We prove the linear orbital stability of spectrally stable stationary discrete shock profiles for conservative finite difference schemes applied to systems of conservation laws. The proof relies on an accurate description of the pointwise…
We study Green functions for the pressure of stationary Stokes systems in a (possibly unbounded) domain $\Omega\subset \mathbb{R}^d$, where $d\ge 2$. We construct the Green function when coefficients are merely measurable in one direction…
The purpose of this article is to establish bounds from below for the life span of regular solutions to the incompressible Navier-Stokes system, whichinvolve norms not only of the initial data, but also of nonlinear functions of the initial…
In the previous paper \cite{J1}, we established pointwise bounds for the Green function of the linearized equation associated with spatially periodic traveling waves $\bar u$ of a system of reaction diffusion equations, and also obtained…
Despite the physical importance, there are limited mathematical theories for the compressible Navier-Stokes equations with strong boundary layers. This is mainly due to the absence of a stream function structure, unlike the extensively…
The basic mathematical properties of Green's functions used in statistical mechanics as well as the equations defining these functions and the techniques of solving these equations are reviewed. An approach is presented called the…
In previous paper derivations of the Green function have been given for 5D off-shell electrodynamics in the framework of the manifestly covariant relativistic dynamics of Stueckelberg (with invariant evolution parameter $\tau$). In this…
We study the dynamics of the two dimensional Navier Stokes equations linearized around a strictly monotonic shear flow on $\mathbb{T}\times\mathbb{R}$. The main task is to understand the associated Rayleigh and Orr-Sommerfeld equations,…
An explicit perturbative solution to all orders is given for a general class of nonlinear differential equations. This solution is written as a sum indexed by rooted trees and uses the Green function of a linearization of the equations. The…
We derive expressions for the electromagnetic Green's function for a layered system using a transfer matrix technique. The expressions we arrive at makes it possible to study symmetry properties of the Green's function, such as reciprocity…
In the plane, we consider the problem of reconstructing a domain from the normal derivative of its Green's function (with fixed pole) relative to the Dirichlet problem for the Laplace operator. By means of the theory of conformal mappings,…
We establish the existence and the pointwise bound of the fundamental solution for the stationary Stokes system with measurable coefficients in the whole space $\mathbb{R}^d$, $d \ge 3$, under the assumption that weak solutions of the…
Using a five dimensional (5D) warped model with two branes along the extra dimension, we study the Green's functions for gauge bosons with a mass gap $m_g = \rho/2$ and a continuum for $s > m_g^2$. We find that the Green's functions exhibit…
Higher Green functions are real-valued functions of two variables on the upper half plane which are bi-invariant under the action of a congruence subgroup, have logarithmic singularity along the diagonal, but instead of the usual equation…
The hydrodynamic stability analysis of gravity-driven, soluble surfactant-laden fluid streaming down a slippery, slanted plane in the presence of external shear force is being explored in this article. The Navier-Stokes equations are…
In this note we present the current status of the derivation of a viscous Serre-Green-Naghdi system. For this goal, the flow domain is separated into two regions. The upper region is governed by inviscid Euler equations, while the bottom…
In this paper, a regression algorithm based on Green's function theory is proposed and implemented. We first survey Green's function for the Dirichlet boundary value problem of 2nd order linear ordinary differential equation, which is a…
A general approach for the calculation of the incoherent intensity scattered by a random medium with rough boundaries has been developed using a Green function formalism. The random medium consists of spherical particles whose physical…
Structure and coordinate dependence of the reflected wave, as well as boundary conditions for quasi-particles of graphene and the two dimensional electron gas in sheets with abrupt lattice edges are obtained and analyzed by the Green's…