In this paper we establish rigorously that the family of Burgers vortices of the three-dimensional Navier-Stokes equation is stable for small Reynolds numbers. More precisely, we prove that any solution whose initial condition is a small perturbation of a Burgers vortex will converge toward another Burgers vortex as time goes to infinity, and we give an explicit formula for computing the change...

this paper presents the results of numerical simulations of the laminar and turbulent flows inside diverging channels using random vortex methods (rvm). random vortex method is a mesh-free method which solves unsteady vorticity equation instead of solving navier-stokes equations directly to determine the velocity field. in this paper, the velocity potential, which is used as the initial conditi...

The motion of a uid subject to Navier{Stokes equations with Coriolis force, to a Robin type traction condition at the surface and to a friction condition at the bottom is investigated. An asymptotic model is derived as the aspect ratio = depth/width of the domain go to 0. When Reynolds number is not too large, this is mathematically justiied and the 3D limit velocity is given in terms of wind, ...

The positivity-preserving property for the inverse of the biharmonic operator under Steklov boundary conditions is studied. It is shown that this property is quite sensitive to the parameter involved in the boundary condition. Moreover, positivity of the Steklov boundary value problem is linked with positivity under boundary conditions of Navier and Dirichlet type.

Abstract. In this paper we introduce a new class of numerical schemes for the incompressible Navier-Stokes equations, which are inspired by the theory of discrete kinetic schemes for compressible fluids. For these approximations it is possible to give a stability condition, based on a discrete velocities version of the Boltzmann H–theorem. Numerical tests are performed to investigate their accu...

A domain in R3 that touches the x3 axis at one point is found with following property. For any initial value a C2 class, axially symmetric Navier Stokes equations slip boundary condition have finite energy solution stays bounded for given time, i.e. no time blow up of fluid velocity occurs. The result seems to be first case where Navier-Stokes regularity problem solved beyond dimension 2.

We establish the existence and multiplicity of solutions for a class of fourth-order superlinear elliptic problems under Navier conditions on the boundary. Here we do not use the Ambrosetti-Rabinowitz condition; instead we assume that the nonlinear term is a nonlinear function which is nonquadratic at infinity.

The paper deals with infinite-dimensional random dynamical systems. Under the condition that the system in question is of mixing type and possesses a random compact attracting set, we show that the support of the unique invariant measure is the minimal random point attractor. The results obtained apply to the randomly forced 2D Navier–Stokes system.

We show that ‖Au+∆u‖L2(Ω) ≤ C1‖∇u‖L2(Ω)+C0‖u‖L2(Ω), where u belongs to the domain of A, the Stokes operator for divergence-free vector fields in the domain Ω ⊂ R satisfying the Navier boundary condition. Moreover, in the case of thin domains, the constant C1 is comparable with the small depth of the domains.

A family of discontinuous Galerkin finite element methods is formulated and analyzed for Stokes and Navier-Stokes problems. An inf-sup condition is established as well as optimal energy estimates for the velocity and L2 estimates for the pressure. In addition, it is shown that the method can treat a finite number of nonoverlapping domains with nonmatching grids at interfaces.