Wall driven steady flow and heat transfer in a porous tube
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...
Water waves generated by disturbances at an ice cover.
Water-wave problem for a vertical shell
The uniqueness theorem is proved for the linearized problem describing radiation and scattering of time-harmonic water waves by a vertical shell having an arbitrary horizontal cross-section. The uniqueness holds for all frequencies, and various locations of the shell are possible: surface-piercing, totally immersed and bottom-standing. A version of integral equation technique is outlined for finding a solution.
Wave growth patterns in a nonlinear dispersive system with instability and dissipation.
Wave loadings on a vertical cylinder due to heave motion.
Waves and wave groups in deep water.
Waves due to initial disturbances at the inertial surface in a stratified fluid of finite depth.
Waves trapped by submerged obstacles at high frequencies.
Wax deposition in crude oils: a new approach
The complex phenomenon of solid wax deposition in wax saturated crude oils subject to thermal gradients has been treated in a number of papers under very specific assumptions (e.g. thermodynamical equilibrium between dissolved wax and the wax suspended in the oil as a crystallized phase). Here we want to consider a more general framework in which thermodynamical equilibrium may not exist, the whole system may form a gel-like structure in which the segregated solid wax has no diffusivity, the thermal...
Weak and classical solutions of equations of motion for third grade fluids
Weak and classical solutions of equations of motion for third grade fluids
This paper shows that the decomposition method with special basis, introduced by Cioranescu and Ouazar, allows one to prove global existence in time of the weak solution for the third grade fluids, in three dimensions, with small data. Contrary to the special case where , studied by Amrouche and Cioranescu, the H1 norm of the velocity is not bounded for all data. This fact, which led others to think, in contradiction to this paper, that the method of decomposition could not apply to...
Weak formulation of free-surface wave equations.
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 for a hyperbolic system with unilateral constraint and mass loss
Weak solutions for a well-posed Hele-Shaw problem
We analyze existence and uniqueness of weak solutions to the well-posed Hele-Shaw problem under general conditions on the fixed boundaries and non-homogeneous governing equation in the unknown domain and non-homogeneous dynamic condition on the free boundary. Our approach allows us also to minimize the restrictions on the boundary and initial data. We derive several estimates on the solutions in spaces, prove a comparison theorem, and show that the solution depends continuously on the initial...
Weak solutions for anisotropic nonlinear elliptic equations with variable exponents.
Weak solutions for steady compressible Navier-Stokes-Fourier system in two space dimensions
We consider steady compressible Navier-Stokes-Fourier system in a bounded two-dimensional domain. We show the existence of a weak solution for arbitrarily large data for the pressure law if and if , , depending on the model for the heat flux.
Weak solutions of a stochastic model for two-dimensional second grade fluids.
Weak solutions of incompressible Euler equations with decreasing energy