Stationary Solutions to the Navier-Stokes Equations in Dimension Four.
Statistical study of Navier-Stokes equations, I
Statistical study of Navier-Stokes equations, II
Statistically stationary solutions to the 3-D Navier-Stokes equation do not show singularities.
Steady Boussinesq system with mixed boundary conditions including friction conditions
In this paper we are concerned with the steady Boussinesq system with mixed boundary conditions. The boundary conditions for fluid may include Tresca slip, leak, one-sided leak, velocity, vorticity, pressure and stress conditions together and the conditions for temperature may include Dirichlet, Neumann and Robin conditions together. For the problem involving the static pressure and stress boundary conditions, it is proved that if the data of the problem are small enough, then there exists a solution...
Steady plane flow of viscoelastic fluid past an obstacle
We consider the steady plane flow of certain classes of viscoelastic fluids in exterior domains with a non-zero velocity prescribed at infinity. We study existence as well as asymptotic behaviour of solutions near infinity and show that for sufficiently small data the solution decays near infinity as fast as the fundamental solution to the Oseen problem.
Steady solutions of the Navier-Stokes equations in unbounded channels and pipes
Steady-state bifurcations of the three-dimensional Kolmogorov problem.
Steady-state thermal Herschel-Bulkley flow with Tresca's friction law.
Stefan problem in a 2D case
The aim of this paper is to analyze the well posedness of the one-phase quasi-stationary Stefan problem with the Gibbs-Thomson correction in a two-dimensional domain which is a perturbation of the half plane. We show the existence of a unique regular solution for an arbitrary time interval, under suitable smallness assumptions on initial data. The existence is shown in the Besov-Slobodetskiĭ class with sharp regularity in the L₂-framework.
Stick-slip transition capturing by using an adaptive finite element method
The numerical modeling of the fully developed Poiseuille flow of a newtonian fluid in a square section with slip yield boundary condition at the wall is presented. The stick regions in outer corners and the slip region in the center of the pipe faces are exhibited. Numerical computations cover the complete range of the dimensionless number describing the slip yield effect, from a full slip to a full stick flow regime. The resolution of variational inequalities describing the flow is based on the...
Stick-slip transition capturing by using an adaptive finite element method
The numerical modeling of the fully developed Poiseuille flow of a Newtonian fluid in a square section with slip yield boundary condition at the wall is presented. The stick regions in outer corners and the slip region in the center of the pipe faces are exhibited. Numerical computations cover the complete range of the dimensionless number describing the slip yield effect, from a full slip to a full stick flow regime. The resolution of variational inequalities describing the flow is based on the...
Stochastic Navier-Stokes equations with artificial compressibility in random durations.
Stokes and Navier–Stokes equations with nonhomogeneous boundary conditions
Stokes efficiency of molecular motor-cargo systems.
Stokes equations in asymptotically flat layers
We study the generalized Stokes resolvent equations in asymptotically flat layers, which can be considered as compact perturbations of an infinite (flat) layer . Besides standard non-slip boundary conditions, we consider a mixture of slip and non-slip boundary conditions on the upper and lower boundary, respectively. We discuss the results on unique solvability of the generalized Stokes resolvent equations as well as the existence of a bounded -calculus for the associated Stokes operator and some...
Stokes flow past a sphere with a source at its centre
Stokes flow past a swarm of porous nanocylindrical particles enclosing a solid core.
Stokeslet and operator extension theory.
Operator version of the Stokeslet method in the theory of creeping flow is suggested. The approach is analogous to the zero-range potential one in quantum mechanics and is based on the theory of self-adjoint operator extensions in the space L2 and in the Pontryagin?s space with an indefinite metric. The problem of Stokes flow in two channels connected through a small opening is considered in the framework of this approach. The case of a periodic system of small openings is studied too. The picture...
Stopping a viscous fluid by a feedback dissipative field: II. The stationary Navier-Stokes problem
We consider a planar stationary flow of an incompressible viscous fluid in a semi-infinite strip governed by the Navier-Stokes system with a feed-back body forces field which depends on the velocity field. Since the presence of this type of non-linear terms is not standard in the fluid mechanics literature, we start by establishing some results about existence and uniqueness of weak solutions. Then, we prove how this fluid can be stopped at a finite distance of the semi-infinite strip entrance by...