On axially symmetric flows in .
On backward-time behavior of the solutions to the 2-D space periodic Navier–Stokes equations
On Bardina and Approximate Deconvolution Models
We first outline the procedure of averaging the incompressible Navier-Stokes equations when the flow is turbulent for various type of filters. We introduce the turbulence model called Bardina’s model, for which we are able to prove existence and uniqueness of a distributional solution. In order to reconstruct some of the flow frequencies that are underestimated by Bardina’s model, we next introduce the approximate deconvolution model (ADM). We prove existence and uniqueness of a “regular weak solution”...
On boundary-driven time-dependent Oseen flows
We consider the single layer potential associated to the fundamental solution of the time-dependent Oseen system. It is shown this potential belongs to L²(0,∞,H¹(Ω)³) and to H¹(0,∞,V') if the layer function is in L²(∂Ω×(0,∞)³). (Ω denotes the complement of a bounded Lipschitz set; V denotes the set of smooth solenoidal functions in H¹₀(Ω)³.) This result means that the usual weak solution of the time-dependent Oseen function with zero initial data and zero body force may be represented by a single...
On bounds of the drag for Stokes flow around a body without thickness
This paper is devoted to lower and upper bounds of the hydrodynamical drag for a body in a Stokes flow. We obtain the upper bound since the solution for a flow in an annulus and therefore the hydrodynamical drag can be explicitly derived. The lower bound is obtained by comparison to the Newtonian capacity of a set and with the help of a result due to J. Simon . The chosen approach provides an interesting lower bound which is independent of the interior of the body.
On computing the pressure by the p version of the finite element method for Stokes problem.
On Conforming Finite Element Methods for the Inhomogeneous Stationary Navier-Stokes Equations.
On Energy Inequality, Smoothness and Large Time Behavior in L2 for Weak Solutions of the Navier-Stokes Equations in Exterior Domains.
On error estimates of some higher order projection and penalty-projection methods for Navier-Stokes equations.
On evolution equations for moving domains.
On evolution inequalities of a modified Navier-Stokes type. III
This is the last from a series of three papers dealing with variational equations of Navier-Stokes type. It is shown that the theoretical results from the preceding parts (existence and regularity of solutions) can be applied to the problem of motion of a fluid through a tube.
On evolution inequalities of a modified Navier-Stokes type. II
The present part of the paper continues the study of the abstract evolution inequality from the first part. Theorem 1 states the existence and uniqueness of a weak solution to the evolution inequality under consideration. The proof is based on the method of approximation of the weak solution by a sequence of strong solutions. Theorem 2 yields two regularity results for the strong solution.
On exact controllability for the Navier-Stokes equations
On exact controllability for the Navier-Stokes equations
We study the local exact controllability problem for the Navier-Stokes equations that describe an incompressible fluid flow in a bounded domain with control distributed in an arbitrary fixed subdomain. The result that we obtain in this paper is as follows. Suppose that we have a given stationary point of the Navier-Stokes equations and our initial condition is sufficiently close to it. Then there exists a locally distributed control such that in a given moment of time the solution of the Navier-Stokes...
On existence and regularity of solutions to a class of generalized stationary Stokes problem
We investigate the existence of weak solutions and their smoothness properties for a generalized Stokes problem. The generalization is twofold: the Laplace operator is replaced by a general second order linear elliptic operator in divergence form and the “pressure” gradient is replaced by a linear operator of first order.
On existence and Schauder regularity of solutions to a class of generalized stationary Stokes problems
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.