Gradient Estimates for Stokes and Navier--Stokes Systems with Piecewise DMO Coefficients

Optimization with the time-dependent Navier-Stokes equations as constraints

In this paper, optimal distributed control of the time-dependent Navier-Stokes equations is considered. The control problem involves the minimization of a measure of the distance between the velocity field and a given target velocity field. A mixed numerical method involving a quasi-Newton algorithm, a novel calculation of the gradients and an inhomogeneous Navier-Stokes solver, to find the opt...

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.

Smoluchowski Navier-Stokes Systems

We discuss equilibria, dynamics and regularity for Smoluchowski equations coupled to Navier-Stokes equations. Introduction We consider mixtures of fluids and microscopic inclusions. The microscopic inclusions are characterized by state variables m ∈ M , where M is a compact smooth Riemannian manifold without boundary. The simplest example is that of microscopic rods with directors m ∈ S. The mi...

On the Navier-stokes Equations with Temperature-dependent Transport Coefficients

Trees for Navier-stokes

We estabilish a representation of the solution of 3d Navier-Stokes equations in the space Φ(α, α) using sums over rooted trees. We study the convergence properties of the series so obtained recovering in a simplified manner some results obtained recently by Sinai and other known results. In particular we extend the series representation of Sinai to the critical case where there exists global so...