Ill-posed Cauchy problems for ideal gas equations and their regularization
Impact of the variations of the mixing length in a first order turbulent closure system
This paper is devoted to the study of a turbulent circulation model. Equations are derived from the “Navier-Stokes turbulent kinetic energy” system. Some simplifications are performed but attention is focused on non linearities linked to turbulent eddy viscosity . The mixing length acts as a parameter which controls the turbulent part in . The main theoretical results that we have obtained concern the uniqueness of the solution for bounded eddy viscosities and small values of and its asymptotic...
Impact of the variations of the mixing length in a first order turbulent closure system
This paper is devoted to the study of a turbulent circulation model. Equations are derived from the “Navier-Stokes turbulent kinetic energy” system. Some simplifications are performed but attention is focused on non linearities linked to turbulent eddy viscosity . The mixing length acts as a parameter which controls the turbulent part in . The main theoretical results that we have obtained concern the uniqueness of the solution for bounded eddy viscosities and small values of and its asymptotic...
Incompressible inviscid limit for the full magnetohydrodynamic flows on expanding domains
In this paper we study the incompressible inviscid limit of the full magnetohydrodynamic flows on expanding domains with general initial data. By applying the relative energy method and carrying out detailed analysis on the oscillation part of the velocity, we prove rigorously that the gradient part of the weak solutions of the full magnetohydrodynamic flows converges to the strong solution of the incompressible Euler system in the whole space, as the Mach number, viscosity as well as the heat conductivity...
Incompressible, inviscid limit of the compressible Navier–Stokes system
Induced trajectories and approximate inertial manifolds
Inégalités de Carleman globales pour les problèmes elliptiques non homogènes
On établit ici, suivant [5], une inégalité de Carleman globale optimale pour les solutions faibles (au sens ) d’équations elliptiques générales avec second membre dans et trace non nulle.La motivation, qui est expliquée dans l’introduction, réside dans l’obtention d’inégalités de Carleman globale pour l’opérateur de Navier-Stokes linéarisé afin, notamment, d’étudier les questions de contrôlabilité exacte sur les trajectoires pour les équations de Navier-Stokes. Une étape majeure consiste à obtenir...
Inf-sup stable nonconforming finite elements of higher order on quadrilaterals and hexahedra
We present families of scalar nonconforming finite elements of arbitrary order with optimal approximation properties on quadrilaterals and hexahedra. Their vector-valued versions together with a discontinuous pressure approximation of order form inf-sup stable finite element pairs of order r for the Stokes problem. The well-known elements by Rannacher and Turek are recovered in the case r=1. A numerical comparison between conforming and nonconforming discretisations will be given. Since higher order...
Initial-boundary value problem for generalized Stokes equations
The paper is concerned with the solvability theory of the generalized Stokes equations arising in the study of the motion of non-Newtonian fluids.
Intégrales premières analytiques des équations différentielles paraboliques non linéaires et du système des équations de Navier-Stokes. Applications à la théorie des solutions statistiques et à d'autres problèmes
Integrated Design of an Active Flow Control System Using a Time-Dependent Adjoint Method
An exploratory study is performed to investigate the use of a time-dependent discrete adjoint methodology for design optimization of a high-lift wing configuration augmented with an active flow control system. The location and blowing parameters associated with a series of jet actuation orifices are used as design variables. In addition, a geometric parameterization scheme is developed to provide a compact set of design variables describing the wing...
Interaction des tourbillons dans les écoulements plans faiblement visqueux
Interior regularity of weak solutions to the perturbed Navier-Stokes equations
In this paper we establish interior regularity for weak solutions and partial regularity for suitable weak solutions of the perturbed Navier-Stokes system, which can be regarded as generalizations of the results in L. Caffarelli, R. Kohn, L. Nirenberg: Partial regularity of suitable weak solutions of the Navier-Stokes equations, Commun. Pure. Appl. Math. 35 (1982), 771–831, and S. Takahashi, On interior regularity criteria for weak solutions of the Navier-Stokes equations, Manuscr. Math. 69...
Interpolation spaces and weighted pseudo almost automorphic solutions to parabolic equations and applications to fluid dynamics
We investigate the existence, uniqueness and polynomial stability of the weighted pseudo almost automorphic solutions to a class of linear and semilinear parabolic evolution equations. The necessary tools here are interpolation spaces and interpolation theorems which help to prove the boundedness of solution operators in appropriate spaces for linear equations. Then for the semilinear equations the fixed point arguments are used to obtain the existence and stability of the weighted pseudo almost...
Intorno ad alcune questioni di meccanica dei fluidi
Invariant sets of solutions of Navier-Stokes and related evolution equations - A survey
Inviscid limit for free-surface Navier-Stokes equations
The aim of this talk is to present recent results obtained with N. Masmoudi on the free surface Navier-Stokes equations with small viscosity.
Inviscid limit for the 2-D stationary Euler system with arbitrary force in simply connected domains
We study the convergence in the vanishing viscosity limit of the stationary incompressible Navier-Stokes equation towards the stationary Euler equation, in the presence of an arbitrary force term. This requires that the fluid is allowed to pass through some open part of the boundary.