In this paper, we prove in two dimensions global identifiability of the viscosity in an incompressible fluid by making boundary measurements. The main contribution of this work is to use more natural boundary measurements, the Cauchy forces, than the Dirichlet-to-Neumann map previously considered in [7] to prove the uniqueness of the viscosity for the Stokes equations and 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

Abstract. In this paper, we study the regularities of solutions of nonlinear stochastic partial differential equations in the framework of Hilbert scales. Then we apply our general result to several typical nonlinear SPDEs such as stochastic Burgers and Ginzburg-Landau’s equations on the real line, stochastic 2D Navier-Stokes equations in the whole space and a stochastic tamed 3D Navier-Stokes ...

Abstract. The procedure of solving the system of the Navier-Stokes equations is proposed. The initial conditions: the velocity divergence (dilatation) being zero and the temperature being the known function, the initial density being constant. The problem is set in the infinite space. The solution of the Navier-Stokes equations was reduced to the solution of integral equations of the Volterra t...

We consider the zero viscosity limit of long time averages of solutions of damped and driven Navier-Stokes equations in R. We prove that the rate of dissipation of enstrophy vanishes. Stationary statistical solutions of the damped and driven Navier-Stokes equations converge to renormalized stationary statistical solutions of the damped and driven Euler equations. These solutions obey the enstro...

We prove Li–Yau-type lower bounds for the eigenvalues of the Stokes operator and give applications to the attractors of the Navier–Stokes equations.

We use the bivariate spline method to solve the time evolution Navier-Stokes equations numerically. The bivariate spline we use in this paper is the spline space of smoothness r and degree 3r over triangulated quadrangulations. The stream function formulation for the Navier-Stokes equations is employed. Galerkin's method is applied to discretize the space variables of the nonlinear fourth order...

The basic concepts and equations of Newtonian Cosmology are presented in the form necessary for the derivation and analysis of the averaged Navier-Stokes-Poisson equations. A particular attention is paid to the physical and cosmological hypotheses about the structure of Newtonian universes. The system of the Navier-StokesPoisson equations governing the cosmological dynamics of Newtonian univers...