Schauder estimates for steady compressible Navier-Stokes equations in bounded domains
Second-order sufficient optimality conditions for the optimal control of Navier-Stokes equations
In this paper sufficient optimality conditions are established for optimal control of both steady-state and instationary Navier-Stokes equations. The second-order condition requires coercivity of the Lagrange function on a suitable subspace together with first-order necessary conditions. It ensures local optimality of a reference function in a -neighborhood, whereby the underlying analysis allows to use weaker norms than .
Second-order sufficient optimality conditions for the optimal control of Navier-Stokes equations
In this paper sufficient optimality conditions are established for optimal control of both steady-state and instationary Navier-Stokes equations. The second-order condition requires coercivity of the Lagrange function on a suitable subspace together with first-order necessary conditions. It ensures local optimality of a reference function in a Ls-neighborhood, whereby the underlying analysis allows to use weaker norms than L∞.
Self-improving bounds for the Navier-Stokes equations
We consider regular solutions to the Navier-Stokes equation and provide an extension to the Escauriaza-Seregin-Sverak blow-up criterion in the negative regularity Besov scale, with regularity arbitrarly close to . Our results rely on turning a priori bounds for the solution in negative Besov spaces into bounds in the positive regularity scale.
Self-similar solutions in weak Lp-spaces of the Navier-Stokes equations.
The most important result stated in this paper is a theorem on the existence of global solutions for the Navier-Stokes equations in Rn when the initial velocity belongs to the space weak Ln(Rn) with a sufficiently small norm. Furthermore, this fact leads us to obtain self-similar solutions if the initial velocity is, besides, an homogeneous function of degree -1. Partial uniqueness is also discussed.
Semi-linearized compressible Navier-Stokes equations perturbed by noise.
Serrin-type regularity criterion for the Navier-Stokes equations involving one velocity and one vorticity component
We consider the Cauchy problem for the three-dimensional Navier-Stokes equations, and provide an optimal regularity criterion in terms of and , which are the third components of the velocity and vorticity, respectively. This gives an affirmative answer to an open problem in the paper by P. Penel, M. Pokorný (2004).
Shape derivatives for general objective functions and the incompressible Navier-Stokes equations
Shape existence in Navier-Stokes flow with heat convection
Sharp asymptotic estimates for vorticity solutions of the 2D Navier-Stokes equation.
Sigma-convergence of stationary Navier-Stokes type equations.
Simulation of instationary, incompressible flows.
Singular limits for the compressible Euler equation in an exterior domain.
Singular limits for the compressible Euler equation in an exterior domain
Solution de l'équation d'Euler en dimension 2
Solution of a spectral problem for the curl and the Stokes operator with periodic boundary conditions.
Solutions auto-similaires des équations de Navier-Stokes
Solutions des équations de Navier-Stokes incompressibles dans un domaine exterieur.
Nous exposons dans cet article l'analogue de ces résultats d'existence pour l'équation de Navier-Stokes [Cannone (4), Cannone et Planchon (27, 5, 28)], mais sur un domaine extérieur Ωε, complémentaire d'un compact à bord lisse. Les deux difficultés nouvelles qui se présentent sont l'absence d'une représentation explicite en Fourier du semi-groupe associé à l'opérateur de Stokes et la nécessité de transposer la notion d'espace de Besov homogène.
Solutions in the large for certain nonlinear parabolic systems
Solutions statistiques homogènes des équations de Navier-Stokes