On the stability of stellar structure in one dimension II : the reactive case
On the stationary Boltzmann equation
For stationary kinetic equations, entropy dissipation can sometimes be used in existence proofs similarly to entropy in the time dependent situation. Recent results in this spirit obtained in collaboration with A. Nouri, are here presented for the nonlinear stationary Boltzmann equation in bounded domains of with given indata and diffuse reflection on the boundary.
On the stationary motion of compressible viscous fluids
On the three-dimensional Euler equations with a free boundary subject to surface tension
On the tidal motion around the earth complicated by the circular geometry of the ocean's shape.
On the uniqueness of solutions in the class of increasing functions of a system describing the dynamics of a viscous weakly stratified fluid in three-dimensional space.
On the variational inequality approach to compressible flows via hodograph method.
We study the flow of a compressible, stationary and irrotational fluid with wake, in a channel, around a convex symmetric profile, with assigned velocity q-infinity at infinity and q-s < q-infinity at the wake. In particular, we study the regularity of the free boundary (for a problem which has non-constant coefficients), in the hodograph plane.
On three-dimensional vortex patches
Ondes centrées et discontinuités de contact globales pour les équations d’Euler axisymétriques de certains gaz parfaits isentropiques en dimension 2 d’espace
Ondes spirales pour le problème de Riemann 2-D d'un fluide compressible
One-dimensional compressible viscous micropolar fluid model: stabilization of the solution for the Cauchy problem.
Optimal control and “strange term" for a Stokes problem in perforated domains.
Optimal control of fluid flow in soil 1. Deterministic case.
We study the numerical aspect of the optimal control of problems governed by a linear elliptic partial differential equation (PDE). We consider here the gas flow in porous media. The observed variable is the flow field we want to maximize in a given part of the domain or its boundary. The control variable is the pressure at one part of the boundary or the discharges of some wells located in the interior of the domain. The objective functional is a balance between the norm of the flux in the observation...
Optimal control of the Primitive Equations of the ocean with Lagrangian observations
We consider an optimal control problem for the three-dimensional non-linear Primitive Equations of the ocean in a vertically bounded and horizontally periodic domain. We aim to reconstruct the initial state of the ocean from Lagrangian observations. This inverse problem is formulated as an optimal control problem which consists in minimizing a cost function representing the least square error between Lagrangian observations and their model counterpart, plus a regularization term. This paper proves...
Parabolic equations with multiple singularities
Parameter estimation for partial differential equations by collage-based numerical approximation.
Periodic solutions arising in ecology of mangroves
Periodic wave solutions for the generalized shallow water wave equation by the improved Jacobi elliptic function method.
Persistance de structures géométriques dans les fluides incompressibles bidimensionnels
Persistance des structures géométriques liées aux poches de tourbillon