Verified numerical computation of solutions for the stationary Navier-Stokes equation in nonconvex polygonal domains

A comparative study between two numerical solutions of the Navier-Stokes equations

The present study aimed to investigate two numerical solutions of the Navier-Stokes equations. For this purpose, the mentioned flow equations were written in two different formulations, namely (i) velocity-pressure and (ii) vorticity-stream function formulations. Solution algorithms and boundary conditions were presented for both formulations and the efficiency of each formulation was investiga...

Numerical Enclosures for Solutions of the Navier-stokes Equation for Small Reynolds Numbers

We describe a method to compute veriied enclosures for solutions of the stationary Navier-Stokes equation in two-dimensional bounded domains. In order to obtain error bounds for numerical approximations , we use the theorem of Newton{Kantorovich. Therefore, we compute approximations for the stream function of the ow and upper bounds of the defect in H ?2 (); we determine an upper bound for the ...

The Navier-Stokes Limit of Stationary Solutions of the Nonlinear Boltzmann Equation

We consider the flow of a gas in a channel whose walls are kept at fixed (different) temperatures. There is a constant external force parallel to the boundaries which may themselves also be moving. The system is described by the stationary Boltzmann equation to which are added Maxwellian boundary conditions with unit accommodation coefficient. We prove that when the temperature gap, the relativ...

Strong Solutions of the Navier-Stokes Equations in Aperture Domains

Nonuniqueness of Generalized Solutions of the Navier-stokes Equation

Solutions of the Cauchy problem for the Navier-Stokes equation, in a certain generalized sense, are not unique.