Decay estimates for the compressible Navier-Stokes equations in unbounded domains.
Décomposition en profils pour les solutions des équations de Navier-Stokes
Decomposition of vector spaces and application to the Stokes problem in arbitrary dimension
Decompositions of Lq and H0 1,q with respect to the operator rot.
Development of local, global, and trace estimates for the solutions of elliptic equations.
Dirichlet control of unsteady Navier–Stokes type system related to Soret convection by boundary penalty method
In this paper, we study the boundary penalty method for optimal control of unsteady Navier–Stokes type system that has been proposed as an alternative for Dirichlet boundary control. Existence and uniqueness of solutions are demonstrated and existence of optimal control for a class of optimal control problems is established. The asymptotic behavior of solution, with respect to the penalty parameter ϵ, is studied. In particular, we prove convergence of solutions of penalized control problem to the...
Dissipation d’énergie pour des solutions faibles des équations d’Euler et Navier-Stokes incompressibles
On étudie l’équation locale de l’énergie pour des solutions faibles des équations d’Euler et Navier-Stokes incompressibles tridimensionnelles. On explicite un terme de dissipation provenant de l’éventuel défaut de régularité de la solution. On donne au passage une preuve simple de la conjecture d’Onsager, améliorant un peu l’hypothèse de [1]. On propose une notion de solution dissipative pour de telles solutions faibles.
Dual-mixed finite element methods for the Navier-Stokes equations
A mixed finite element method for the Navier–Stokes equations is introduced in which the stress is a primary variable. The variational formulation retains the mathematical structure of the Navier–Stokes equations and the classical theory extends naturally to this setting. Finite element spaces satisfying the associated inf–sup conditions are developed.
Dynamical shape control in non-cylindrical Navier-Stokes equations.
Dynamics of Singularity Surfaces for Compressible Navier-Stokes Flows in Two Space Dimensions
We prove the global existence of solutions of the Navier-Stokes equations of compressible, barotropic flow in two space dimensions with piecewise smooth initial data. These solutions remain piecewise smooth for all time, retaining simple jump discontinuities in the density and in the divergence of the velocity across a smooth curve, which is convected with the flow. The strengths of these discontinuities are shown to decay exponentially in time, more rapidly for larger acoustic speeds and smaller...