This paper continues the development of the least-squares methodology for the solution of the incompressible Navier-Stokes equations started in Part I. Here we again use a velocityflux first-order Navier-Stokes system, but our focus now is on a practical algorithm based on a discrete negative norm.

We study spatial analyticity properties of solutions of the Navier-Stokes equation and obtain new growth rate estimates for the analyticity radius. We also study stability properties of strong global solutions of the Navier-Stokes equation with data in H, r ≥ 1/2 and prove a stability result for the analyticity radius.

On Schwarz's domain decomposition methods for elliptic boundary value problems, submitted for publication, 1996. 6. M. J. Lai and P. Wenston, Bivariate spline method for numerical solution of steady state Navier-Stokes equations over polygons in stream function formulation, submitted, 1997. Bivariate spline method for numerical solution of time evolution Navier-Stokes equations over polygons in

We consider an inverse problem of determining a spatially varying factor in a source term in a nonstationary linearized Navier-Stokes equations by observation data in an arbitrarily fixed sub-domain over some time interval. We prove the Lipschitz stability provided that the t-dependent factor satisfies a non-degeneracy condition. Our proof based on a new Carleman estimate for the Navier-Stokes ...

In this paper we show the existence of regular solutions of the Rothe–approximation of the unsteady Navier–Stokes equations with periodic boundary condition in arbitrary dimension. The result relies on techniques developed by the authors in the study of the higher–dimensional steady Navier–Stokes equations.

We consider the incompressible Navier-Stokes equations with spatially periodic boundary conditions. If the Reynolds number is small enough we provide an elementary short proof of the existence of global in time Hölder continuous solutions. Our proof is based on the stochastic Lagrangian formulation of the Navier-Stokes equations, and works in both the two and three dimensional situation.

In this paper we consider the three–dimensional Navier–Stokes equations in an infinite channel. We provide a sufficient condition, in terms of ∂zp, where p is the pressure, for the global existence of the strong solutions to the three–dimensional Navier–Stokes equations. AMS Subject Classifications: 35Q35, 65M70

We establish a connection between the strong solution to the spatially periodic Navier–Stokes equations and a solution to a system of forward-backward stochastic differential equations (FBSDEs) on the group of volume-preserving diffeomorphisms of a flat torus. We construct a representation of the strong solution to the Navier–Stokes equations in terms of diffusion processes.

We obtain a pointwise, a priori bound for the vorticity of axis symmetric solutions to the 3 dimensional Navier-Stokes equations. The bound is in the form of a reciprocal of a power of the distance to the axis of symmetry. This seems to be the first general pointwise estimate established for the axis symmetric Navier-Stokes equations.

In this paper we establish the local exact internal controllability of steady state solutions for the Navier-Stokes equations in three-dimensional bounded domains, with the Navier slip boundary conditions. The proof is based on a Carlemantype estimate for the backward Stokes equations with the same boundary conditions, which is also established here.