A criterion is given for the convergence of numerical solutions of the Navier-Stokes equations in two dimensions under steady conditions. The criterion applies to all cases, of steady viscous flow in two dimensions and shows that if the local ' mesh Reynolds number ', based on the size of the mesh used in the solution, exceeds a certain fixed value, the numerical solution will not converge.

On the Navier-Stokes equations

In this chapter we introduce some basic notation and definitions. We discuss a few general results on interpolation spaces. The most important one is the Aronszajn-Gagliardo theorem.

General Properties of Interpolation Spaces

Theory Of Function Spaces Ii

Solutions for semilinear parabolic equations in L[p] and regularity of weak solutions of the Navier-Stokes system

『Introduction to PDEs and Waves for the Atmosphere and Ocean(Courant Lecture Notes, Volume 9)』, Andrew Majda著, American Mathematical Society刊, 2003年1月発行, 234頁, ペーパーバック, $40.95, ISBN:0-8218-2954-8

We consider a two-component Camassa–Holm system which arises in shallow water theory. We analyze a wave breaking mechanism and the global existence of solutions. First, we discuss the local well posedness and a blow up mechanism, then establish some new blow up criteria for this system formulated either on the line or with space-periodic initial conditions. Finally, the existence of global solutions is analyzed.

On Solutions to a Two‐Component Generalized Camassa‐Holm Equation

Blow-up and global solutions to a new integrable model with two components

Some new regularity criteria for the 3D MHD equations

A remark on the regularity criterion of Boussinesq equations with zero heat conductivity

In this paper we establish some new logarithmically improved regularity criteria for the Navier–Stokes equations in the homogeneous Besov space B∞,∞−1.

Zhengguang Guo

Papers

On Solutions to a Two‐Component Generalized Camassa‐Holm Equation

Blow-up and global solutions to a new integrable model with two components

Some new regularity criteria for the 3D MHD equations

A remark on the regularity criterion of Boussinesq equations with zero heat conductivity

Remarks on logarithmical regularity criteria for the Navier-Stokes equations