$L_q-L_r$-Estimates for Non-Stationary Stokes Equations in an Aperture Domain

The Stationary Navier-Stokes Equations

Having considered the linear Stokes equations, we will now bring back the nonlinear term and consider the nonlinear version of the Stokes system. The solution of these equations can be viewed as the limit to which the solution of the full N-S equations tends as t tends to infinity. Of course no one knows at this point if the solutions of the N-S equations do tend to some limit as t tends to inf...

On a number of algorithms for solving non-stationary Stokes and Navier-Stokes equations

On a number of algorithms for solving non-stationary Stokes and Navier-Stokes equations

An H1 setting for the Navier-Stokes equations: quantitative estimates

We consider the incompressible Navier-Stokes (NS) equations on a torus, in the setting of the spaces L2 and H1; our approach is based on a general framework for semior quasi-linear parabolic equations proposed in the previous work [9]. We present some estimates on the linear semigroup generated by the Laplacian and on the quadratic NS nonlinearity; these are fully quantitative, i.e., all the co...

Analyticity estimates for the Navier-Stokes equations

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.