On existence of a boundary layer near a three-phase contact point.
On existence of solutions for the nonstationary Stokes system with boundary slip conditions
Existence of solutions for equations of the nonstationary Stokes system in a bounded domain Ω ⊂ ℝ³ is proved in a class such that velocity belongs to , and pressure belongs to for p > 3. The proof is divided into three steps. First, the existence of solutions with vanishing initial data is proved in a half-space by applying the Marcinkiewicz multiplier theorem. Next, we prove the existence of weak solutions in a bounded domain and then we regularize them. Finally, the problem with nonvanishing...
On finite element approximation of flow induced vibration of elastic structure
In this paper the fluid-structure interaction problem is studied on a simplified model of the human vocal fold. The problem is mathematically described and the arbitrary Lagrangian-Eulerian method is applied in order to treat the time dependent computational domain. The viscous incompressible fluid flow and linear elasticity models are considered. The fluid flow and the motion of elastic body is approximated with the aid of finite element method. An attention is paid to the applied stabilization...
On Finite Element Subspaces over Quadrilateral and Hexahedral Meshes for Incompressible Viscous Flow Problems.
On fully developed flows of fluids with a pressure dependent viscosity in a pipe
Stokes recognized that the viscosity of a fluid can depend on the normal stress and that in certain flows such as flows in a pipe or in channels under normal conditions, this dependence can be neglected. However, there are many other flows, which have technological significance, where the dependence of the viscosity on the pressure cannot be neglected. Numerous experimental studies have unequivocally shown that the viscosity depends on the pressure, and that this dependence can be quite strong,...
On generalized energy equality of the Navier-Stokes equations.
On geometrical properties of free boundaries in the Hele-Shaw flow moving boundary problem.
On global regular solutions to the Navier-Stokes equations with heat convection
Global existence of regular solutions to the Navier-Stokes equations for velocity and pressure coupled with the heat convection equation for temperature in a cylindrical pipe is shown. We assume the slip boundary conditions for velocity and the Neumann condition for temperature. First we prove long time existence of regular solutions in [kT,(k+1)T]. Having T sufficiently large and imposing some decay estimates on , we continue the local solutions step by step up to a global one.
On inhomogeneous incompressible fluids and reverse Hölder inequalities
On Large Eddy Simulation and Variational Multiscale Methods in the numerical simulation of turbulent incompressible flows
Numerical simulation of turbulent flows is one of the great challenges in Computational Fluid Dynamics (CFD). In general, Direct Numerical Simulation (DNS) is not feasible due to limited computer resources (performance and memory), and the use of a turbulence model becomes necessary. The paper will discuss several aspects of two approaches of turbulent modeling—Large Eddy Simulation (LES) and Variational Multiscale (VMS) models. Topics which will be addressed are the detailed derivation of these...
On Lipschitz truncations of Sobolev functions (with variable exponent) and their selected applications
We study properties of Lipschitz truncations of Sobolev functions with constant and variable exponent. As non-trivial applications we use the Lipschitz truncations to provide a simplified proof of an existence result for incompressible power-law like fluids presented in [Frehse et al., SIAM J. Math. Anal34 (2003) 1064–1083]. We also establish new existence results to a class of incompressible electro-rheological fluids.
On local existence of solutions of the free boundary problem for an incompressible viscous self-gravitating fluid motion
The local-in-time existence of solutions of the free boundary problem for an incompressible viscous self-gravitating fluid motion is proved. We show the existence of solutions with lowest possible regularity for this problem such that with r>3. The existence is proved by the method of successive approximations where the solvability of the Cauchy-Neumann problem for the Stokes system is applied. We have to underline that in the -approach the Lagrangian coordinates must be used. We are looking...
On noncompact free boundary problems for the plae stationary Navier-Stokes equations.
On non-homogeneous viscous incompressible fluids. Existence of regular solutions
We consider the flow of a non-homogeneous viscous incompressible fluid which is known at an initial time. Our purpose is to prove that, when is smooth enough, there exists a local strong regular solution (which is global for small regular data).
On nonoverlapping domain decomposition methods for the incompressible Navier-Stokes equations
In this paper, a Dirichlet-Neumann substructuring domain decomposition method is presented for a finite element approximation to the nonlinear Navier-Stokes equations. It is shown that the Dirichlet-Neumann domain decomposition sequence converges geometrically to the true solution provided the Reynolds number is sufficiently small. In this method, subdomain problems are linear. Other version where the subdomain problems are linear Stokes problems is also presented.
On nonoverlapping domain decomposition methods for the incompressible Navier-Stokes equations
In this paper, a Dirichlet-Neumann substructuring domain decomposition method is presented for a finite element approximation to the nonlinear Navier-Stokes equations. It is shown that the Dirichlet-Neumann domain decomposition sequence converges geometrically to the true solution provided the Reynolds number is sufficiently small. In this method, subdomain problems are linear. Other version where the subdomain problems are linear Stokes problems is also presented.
On nonstationary Stokes problem in exterior domains
On nonsymmetric two-dimensional viscous flow through an aperture.
On numerical solution of the incompressible Navier-Stokes equations with static or total pressure specified on boundaries.
On Optimum Regularity of Navier-Stokes Solutions at Time t = 0.