Harmonic analysis tools for solving the incompressible Navier-Stokes equations
نویسنده
چکیده
Introduction Section 1: Preliminaries 1.1 The Navier-Stokes equations 1.2 Classical, mild and weak solutions 1.3 Navier meets Fourier Section 2: Functional setting of the equations 2.1 The Littlewood-Paley decomposition 2.2 The Besov spaces 2.3 The paraproduct rule 2.4 The wavelet decomposition 2.5 Other useful function spaces Section 3: Existence theorems 3.1 The fixed point theorem 3.2 Scaling invariance 3.3 Super-critical case
منابع مشابه
An analytical formula and FEM simulations for the viscous damping of a periodic perforated MEMS microstructure outside the lubrication approximation
The article presents an axi-symmetrical model for determining the total damping coefficient of a periodic perforated microelectromechanical systems (MEMS) microstructure for cases where the lubrication approximation yielding the Reynolds’ equation is no longer appropriate. Damping is modeled by solving for the viscous flow in an approximation of the periodic cell geometry using an equivalent ax...
متن کاملAn Enhanced Flux Treatment in Solving Incompressible Flow in a Forward-Facing Step
The aim of this paper is to give a detailed effect of several parameters such as step height, Reynolds number, contraction ratio, and temperature difference between the entrance and solid boundaries, of a forward-facing step. An accurate length of separation and reattachment zones are achieved. A finite-volume method (FVM) has been developed to study incompressible flow in a forward-facing step...
متن کاملFirst-order system least squares for the Oseen equations
Following earlier work for Stokes equations, a least-squares functional is developed for twoand three-dimensional Oseen equations. By introducing a velocity flux variable and associated curl and trace equations, ellipticity is established in an appropriate product norm. The form of Oseen equations examined here is obtained by linearizing the incompressible Navier-Stokes equations. An algorithm ...
متن کاملThe Meshless Local Petrov-Galerkin (MLPG) Method for Solving Incompressible Navier-Stokes Equations
The truly Meshless Local Petrov-Galerkin (MLPG) method is extended to solve the incompressible Navier-Stokes equations. The local weak form is modified in a very careful way so as to ovecome the so-called Babus̃ka-Brezzi conditions. In addition, The upwinding scheme as developed in Lin and Atluri (2000a) and Lin and Atluri (2000b) is used to stabilize the convection operator in the streamline di...
متن کاملA Relaxed Splitting Preconditioner for the Incompressible Navier-Stokes Equations
A relaxed splitting preconditioner based on matrix splitting is introduced in this paper for linear systems of saddle point problem arising from numerical solution of the incompressible NavierStokes equations. Spectral analysis of the preconditioned matrix is presented, and numerical experiments are carried out to illustrate the convergence behavior of the preconditioner for solving both steady...
متن کامل