Viscous-inviscid coupled problem with interfacial data.
Vorticity dynamics and numerical resolution of Navier-Stokes equations
We present a new methodology for the numerical resolution of the hydrodynamics of incompressible viscid newtonian fluids. It is based on the Navier-Stokes equations and we refer to it as the vorticity projection method. The method is robust enough to handle complex and convoluted configurations typical to the motion of biological structures in viscous fluids. Although the method is applicable to three dimensions, we address here in detail only the two dimensional case. We provide numerical data...
Vorticity dynamics and numerical Resolution of Navier-Stokes Equations
We present a new methodology for the numerical resolution of the hydrodynamics of incompressible viscid newtonian fluids. It is based on the Navier-Stokes equations and we refer to it as the vorticity projection method. The method is robust enough to handle complex and convoluted configurations typical to the motion of biological structures in viscous fluids. Although the method is applicable to three dimensions, we address here in detail only the two dimensional case. We provide numerical data...
Wall laws for viscous fluids near rough surfaces
In this paper, we review recent results on wall laws for viscous fluids near rough surfaces, of small amplitude and wavelength ε. When the surface is “genuinely rough”, the wall law at first order is the Dirichlet wall law: the fluid satisfies a “no-slip” boundary condition on the homogenized surface. We compare the various mathematical characterizations of genuine roughness, and the corresponding homogenization results. At the next order, under...
Weak solutions for a fluid-elastic structure interaction model.
The purpose of this paper is to study a model coupling an incompressible viscous fiuid with an elastic structure in a bounded container. We prove the existence of weak solutions à la Leray as long as no collisions occur.
Weak solutions of a stochastic model for two-dimensional second grade fluids.
Weak solutions to the Navier-Stokes equations in a Y-shaped domain
We prove the existence of weak solutions to the Navier-Stokes equations describing the motion of a fluid in a Y-shaped domain.
Weakly continuous operators. Applications to differential equations
The paper is a supplement to a survey by J. Franců: Monotone operators, A survey directed to differential equations, Aplikace Matematiky, 35(1990), 257–301. An abstract existence theorem for the equation with a coercive weakly continuous operator is proved. The application to boundary value problems for differential equations is illustrated on two examples. Although this generalization of monotone operator theory is not as general as the M-condition, it is sufficient for many technical applications....
Weighted L² and approaches to fluid flow past a rotating body
Consider the flow of a viscous, incompressible fluid past a rotating obstacle with velocity at infinity parallel to the axis of rotation. After a coordinate transform in order to reduce the problem to a Navier-Stokes system on a fixed exterior domain and a subsequent linearization we are led to a modified Oseen system with two additional terms one of which is not subordinate to the Laplacean. In this paper we describe two different approaches to this problem in the whole space case. One of them...
Wellposedness and stability results for the Navier-Stokes equations in
Well-posedness for density-dependent incompressible fluids with non-Lipschitz velocity
This paper is dedicated to the study of the initial value problem for density dependent incompressible viscous fluids in with . We address the question of well-posedness for large and small initial data having critical Besov regularity in functional spaces as close as possible to the ones imposed in the incompressible Navier Stokes system by Cannone, Meyer and Planchon (where with ). This improves the classical analysis where is considered belonging in such that the velocity remains...
Wellposedness for the system modelling the motion of a rigid body of arbitrary form in an incompressible viscous fluid
In this paper, we consider the interaction between a rigid body and an incompressible, homogeneous, viscous fluid. This fluid-solid system is assumed to fill the whole space , or . The equations for the fluid are the classical Navier-Stokes equations whereas the motion of the rigid body is governed by the standard conservation laws of linear and angular momentum. The time variation of the fluid domain (due to the motion of the rigid body) is not known a priori, so we deal with a free boundary...
Well-posedness issues for the Prandtl boundary layer equations
These notes are an introduction to the recent paper [7], about the well-posedness of the Prandtl equation. The difficulties and main ideas of the paper are described on a simpler linearized model.
Well-posedness of the Euler and Navier-Stokes equations in the Lebesque spaces Lsp(R2).
In this paper we show that the Euler equation for incompressible fluids in R2 is well posed in the (vector-valued) Lebesgue spacesLsp = (1 - ∆)-s/2 Lp(R2) with s > 1 + 2/p, 1 < p < ∞and that the same is true of the Navier-Stokes equation uniformly in the viscosity ν.
Wetting on rough surfaces and contact angle hysteresis: numerical experiments based on a phase field model
We present a phase field approach to wetting problems, related to the minimization of capillary energy. We discuss in detail both the Γ-convergence results on which our numerical algorithm are based, and numerical implementation. Two possible choices of boundary conditions, needed to recover Young's law for the contact angle, are presented. We also consider an extension of the classical theory of capillarity, in which the introduction of a dissipation mechanism can explain and predict the hysteresis...
Zero Mach number limit in critical spaces for compressible Navier–Stokes equations
Автомодельные решения задач растекания и выдавливания слоя нелинейно- вязкой жидкости
Асимптотическое решение задачи Навье-Стокса o течении тонкого слоя жидкости.
Вынужденные колебания столба ньютоновской жидкости в трубке, герметизированной мембранами
Граничные экстремальные задачи динамики вязкой несжимаемой жидкости