Unsteady motion around a uniformly deforming rotating cylinder
Validation of numerical simulations of a simple immersed boundary solver for fluid flow in branching channels
This work deals with the flow of incompressible viscous fluids in a two-dimensional branching channel. Using the immersed boundary method, a new finite difference solver was developed to interpret the channel geometry. The numerical results obtained by this new solver are compared with the numerical simulations of the older finite volume method code and with the results obtained with OpenFOAM. The aim of this work is to verify whether the immersed boundary method is suitable for fluid flow in channels...
Vanishing viscosity limit for an expanding domain in space
Very weak solutions of the stationary Stokes equations in unbounded domains of half space type
We consider the theory of very weak solutions of the stationary Stokes system with nonhomogeneous boundary data and divergence in domains of half space type, such as , bent half spaces whose boundary can be written as the graph of a Lipschitz function, perturbed half spaces as local but possibly large perturbations of , and in aperture domains. The proofs are based on duality arguments and corresponding results for strong solutions in these domains, which have to be constructed in homogeneous...
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....
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.
Zero Mach number limit in critical spaces for compressible Navier–Stokes equations
Асимптотическое решение задачи Навье-Стокса o течении тонкого слоя жидкости.
Граничные экстремальные задачи динамики вязкой несжимаемой жидкости
Задача со свободной границей для уравнения Навье-Стокса для сжимаемой жидкости при наличии поверхностного натяжения
К вопросу о разрешимости краевых и начально-краевых задач для уравнений Навье-Стокса в областях с некомпактными границами
К задаче о нормальных колебаниях тяжелой вязкой жидкости в сосуде.