On the Navier-Stokes Equations in Non-Cylindrical Domains: On the Existence and Regularity.
On the Navier-Stokes equations with anisotropic wall slip conditions
This article deals with the solvability of the boundary-value problem for the Navier-Stokes equations with a direction-dependent Navier type slip boundary condition in a bounded domain. Such problems arise when steady flows of fluids in domains with rough boundaries are approximated as flows in domains with smooth boundaries. It is proved by means of the Galerkin method that the boundary-value problem has a unique weak solution when the body force and the variability of the surface friction are...
On the Navier-Stokes equations with temperature-dependent transport coefficients.
On the Numerical Treatment of Viscous Flows Against Bodies with Corners and Edges by Boundary Element and Multigrid Methods.
On the parameter in augmented Lagrangian preconditioning for isogeometric discretizations of the Navier-Stokes equations
In this paper, we deal with the optimal choice of the parameter for augmented Lagrangian preconditioning of GMRES method for efficient solution of linear systems obtained from discretization of the incompressible Navier-Stokes equations. We consider discretization of the equations using the B-spline based isogeometric analysis approach. We are interested in the dependence of the convergence on the parameter for various problem parameters (Reynolds number, mesh refinement) and especially for...
On the Regularity Conditions for the Navier-Stokes and Related Equations.
On the regularity of the stationary Navier-Stokes equations
On the result of He concerning the smoothness of solutions to the Navier-Stokes equations.
On the Stability of Bilinear-Constant Velocity-Pressure Finite Elements.
On the stability of the coupling of 3D and 1D fluid-structure interaction models for blood flow simulations
We consider the coupling between three-dimensional (3D) and one-dimensional (1D) fluid-structure interaction (FSI) models describing blood flow inside compliant vessels. The 1D model is a hyperbolic system of partial differential equations. The 3D model consists of the Navier-Stokes equations for incompressible Newtonian fluids coupled with a model for the vessel wall dynamics. A non standard formulation for the Navier-Stokes equations is adopted to have suitable boundary conditions for the...
On the structure of flows through pipe-like domains satisfying a geometrical constraint
We study solutions of the steady Navier-Stokes equations in a bounded 2D domain with the slip boundary conditions admitting flow across the boundary. We show conditions guaranteeing uniqueness of the solution. Next, we examine the structure of the solution considering an approximation given by a natural linearization. Suitable error estimates are also obtained.
On the Transport-Diffusion Algorithm and Its Applications to the NavierStokes Equations.
On the asymptotic properties of solutions of the Navier-Stokes equations in the half-space.
On unsteady two-phase fluid flow due to eccentric rotation of a disk.
On weak solutions of steady Navier-Stokes equations for monatomic gas
We use estimates for the inverse Laplacian of the pressure introduced by Plotnikov, Sokolowski and Frehse, Goj, Steinhauer together with the nonlinear potential theory due to Adams, Hedberg, to get a priori estimates and to prove existence of weak solutions to steady isentropic Navier-Stokes equations with the adiabatic constant for the flows powered by volume non-potential forces and with for the flows powered by potential forces and arbitrary non-volume forces. According to our knowledge,...
On weak solutions to the equations of non-stationary motion of heat-conducting incompressible viscous fluids: defect measure and energy equality
We consider the non-stationary Navier-Stokes equations completed by the equation of conservation of internal energy. The viscosity of the fluid is assumed to depend on the temperature, and the dissipation term is the only heat source in the conservation of internal energy. For the system of PDE's under consideration, we prove the existence of a weak solution such that: 1) the weak form of the conservation of internal energy involves a defect measure, and 2) the equality for the total energy is satisfied....
Optimal design of stationary flow problems by path-following interior-point methods
Optimal error estimates for the Stokes and Navier-Stokes equations with slip-boundary condition
Optimal error Estimates for the Stokes and Navier–Stokes equations with slip–boundary condition
We consider a finite element discretization by the Taylor–Hood element for the stationary Stokes and Navier–Stokes equations with slip boundary condition. The slip boundary condition is enforced pointwise for nodal values of the velocity in boundary nodes. We prove optimal error estimates in the H1 and L2 norms for the velocity and pressure respectively.
Optimale lokale Existenzsätze für die Gleichungen von Navier-Stokes.