The aim of this dissertation is to study stochastic Navier-Stokes equations with a fractional Brownian motion noise. The second chapter will introduce the background results on fractional Brownian motions and some of their properties. The third chapter will focus on the Stokes operator and the semigroup generated by this operator. The Navier-Stokes equations and the evolution equation setup wil...

The incompressible Navier-Stokes equations are discretized in space and integrated in time by the method of lines and a semi-implicit method. In each time step a set of systems of linear equations has to be solved. The size of the time steps are restricted by stability and accuracy of the time-stepping scheme, and convergence of the iterative methods for the solution of the systems of equations...

In this paper statistical solutions of the 3D Navier-Stokes-α model with periodic boundary condition are considered. It is proved that under certain natural conditions statistical solutions of the 3D Navier-Stokes-α model converge to statistical solutions of the exact 3D Navier-Stokes equations as α goes to zero. The statistical solutions considered here arise as families of time-projections of...

The applicability of three numerical approximation methods of solving the Navier-Stokes equations (local stagnation streamline approximation, ‘parabolized’ equations, and the thin-viscous-shock-layer approach) have been analyzed to study nonequilibrium hypersonic viscous flows near blunt bodies. These approximations allow reducing the calculation time by factor of 10 in comparison with the time...

The additive turbulent decomposition (ATD) method is a computational scheme for solving the Navier–Stokes equations and related nonlinear dissipative evolution equations. It involves a decomposition of the Navier–Stokes equation into equations for largeand small-scale components similar in spirit, but different in details, to the nonlinear Galerkin methods proposed by Temam and coworkers. In th...

We consider the vanishing viscosity limit of the Navier-Stokes equations in a half space, with Dirichlet boundary conditions. We prove that the inviscid limit holds in the energy norm if the product of the components of the Navier-Stokes solutions are equicontinuous at x2 = 0. A sufficient condition for this to hold is that the tangential Navier-Stokes velocity remains uniformly bounded and has...

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...