Spectral Tau Approximation of the Two-Dimensional Stokes Problem.
Stabilité et asymptotique en temps grand de solutions globales des équations de Navier-Stokes
We study a priori global strong solutions of the incompressible Navier-Stokes equations in three space dimensions. We prove that they behave for large times like small solutions, and in particular they decay to zero as time goes to infinity. Using that result, we prove a stability theorem showing that the set of initial data generating global solutions is open.
Stability estimate for strong solutions of the Navier-Stokes system and its applications.
Stability for a certain class of numerical methods – abstract approach and application to the stationary Navier-Stokes equations
We consider some abstract nonlinear equations in a separable Hilbert space and some class of approximate equations on closed linear subspaces of . The main result concerns stability with respect to the approximation of the space . We prove that, generically, the set of all solutions of the exact equation is the limit in the sense of the Hausdorff metric over of the sets of approximate solutions, over some filterbase on the family of all closed linear subspaces of . The abstract results are...
Stability of a finite element method for 3D exterior stationary Navier-Stokes flows
We consider numerical approximations of stationary incompressible Navier-Stokes flows in 3D exterior domains, with nonzero velocity at infinity. It is shown that a P1-P1 stabilized finite element method proposed by C. Rebollo: A term by term stabilization algorithm for finite element solution of incompressible flow problems, Numer. Math. 79 (1998), 283–319, is stable when applied to a Navier-Stokes flow in a truncated exterior domain with a pointwise boundary condition on the artificial boundary....
Stability of Constant Solutions to the Navier-Stokes System in ℝ³
The paper examines the initial value problem for the Navier-Stokes system of viscous incompressible fluids in the three-dimensional space. We prove stability of regular solutions which tend to constant flows sufficiently fast. We show that a perturbation of a regular solution is bounded in for k ∈ ℕ. The result is obtained under the assumption of smallness of the L₂-norm of the perturbing initial data. We do not assume smallness of the -norm of the perturbing initial data or smallness of the...
Stability of oscillating boundary layers in rotating fluids
We prove the linear and non-linear stability of oscillating Ekman boundary layers for rotating fluids in the so-called ill-prepared case under a spectral hypothesis. Here, we deal with the case where the viscosity and the Rossby number are both equal to . This study generalizes the study of [23] where a smallness condition was imposed and the study of [26] where the well-prepared case was treated.
Stability with respect to domain of the low Mach number limit of compressible heat-conducting viscous fluid
We investigate the asymptotic limit of solutions to the Navier-Stokes-Fourier system with the Mach number proportional to a small parameter , the Froude number proportional to and when the fluid occupies large domain with spatial obstacle of rough surface varying when . The limit velocity field is solenoidal and satisfies the incompressible Oberbeck–Boussinesq approximation. Our studies are based on weak solutions approach and in order to pass to the limit in a convective term we apply the spectral...
Starlike log-harmonic mappings of order .
Stationary Solutions to the Navier-Stokes Equations in Dimension Four.
Stationary states and moving planes
Most of the paper deals with the application of the moving plane method to different questions concerning stationary accumulations of isentropic gases. The first part compares the concepts of stationarity arising from the points of view of dynamics and the calculus of variations. Then certain stationary solutions are shown to be unstable. Finally, using the moving plane method, a short proof of the existence of energy-minimizing gas balls is given.
Statistical study of Navier-Stokes equations, I
Statistical study of Navier-Stokes equations, II
Statistically stationary solutions to the 3-D Navier-Stokes equation do not show singularities.
Steady compressible Navier-Stokes-Fourier system in two space dimensions
We study steady flow of a compressible heat conducting viscous fluid in a bounded two-dimensional domain, described by the Navier-Stokes-Fourier system. We assume that the pressure is given by the constitutive equation , where is the density and is the temperature. For , we prove existence of a weak solution to these equations without any assumption on the smallness of the data. The proof uses special approximation of the original problem, which guarantees the pointwise boundedness of the...
Steady compressible Oseen flow with slip boundary conditions
We prove the existence of solution in the class H²(Ω) × H¹(Ω) to the steady compressible Oseen system with slip boundary conditions in a two dimensional, convex domain with boundary of class . The method is to regularize a weak solution obtained via the Galerkin method. The problem of regularization is reduced to the problem of solvability of a certain transport equation by application of the Helmholtz decomposition. The method works under an additional assumption on the geometry of the boundary....
Steady-state bifurcations of the three-dimensional Kolmogorov problem.
Stochastic Lagrangian method for downscaling problems in computational fluid dynamics
This work aims at introducing modelling, theoretical and numerical studies related to a new downscaling technique applied to computational fluid dynamics. Our method consists in building a local model, forced by large scale information computed thanks to a classical numerical weather predictor. The local model, compatible with the Navier-Stokes equations, is used for the small scale computation (downscaling) of the considered fluid. It is inspired by Pope's works on turbulence, and consists in...
Stokes and Navier–Stokes equations with nonhomogeneous boundary conditions
Stokes equations in asymptotically flat layers
We study the generalized Stokes resolvent equations in asymptotically flat layers, which can be considered as compact perturbations of an infinite (flat) layer . Besides standard non-slip boundary conditions, we consider a mixture of slip and non-slip boundary conditions on the upper and lower boundary, respectively. We discuss the results on unique solvability of the generalized Stokes resolvent equations as well as the existence of a bounded -calculus for the associated Stokes operator and some...