Existence of solutions for the two-dimensional stationary Euler system for ideal fluids with arbitrary force
Existence of strong solutions for nonisothermal Korteweg system
This work is devoted to the study of the initial boundary value problem for a general non isothermal model of capillary fluids derived by J. E Dunn and J. Serrin (1985) in [9, 16], which can be used as a phase transition model.We distinguish two cases, when the physical coefficients depend only on the density, and the general case. In the first case we can work in critical scaling spaces, and we prove global existence of solution and uniqueness for data close to a stable equilibrium. For general...
Existence of threedimensional, steady, inviscid, incompressible flows with nonvanishing vorticity.
Existence of weak solutions for a nonhomogeneous solidification mathematical model.
Existence of weak solutions for a nonlinear elliptic system.
Existence results for a nonlinear problem modeling the displacement of a solid in a transverse flow
Existence results for mean field equations
Existence results for the flow of viscoelastic fluids of White-Metzner type.
This work is concerned with the study of the flow of an incompressible viscoelastic fluid of White-Metzner type. These models lead to systems of partial differential equations that are evolutionary, are globally well posed. The objective of this article is to prove the local and global existence of solutions of these systems.
Existence, uniqueness, and quasilinearization results for nonlinear differential equations arising in viscoelastic fluid flow.
Exponential attractors for a nonclassical diffusion equation.
Exponential convergence to the stationary measure and hyperbolicity of the minimisers for random Lagrangian Systems
We consider a class of 1d Lagrangian systems with random forcing in the spaceperiodic setting: These systems have been studied since the 1990s by Khanin, Sinai and their collaborators [7, 9, 11, 12, 15]. Here we give an overview of their results and then we expose our recent proof of the exponential convergence to the stationary measure [6]. This is the first such result in a classical setting, i.e. in the dual-Lipschitz metric with respect to the Lebesgue space for finite , partially answering...
Extension of a regularity result concerning the dam problem
One proves, in the case of piecewise smooth coefficients, that the time derivative of the solution of the so called dam problem is a measure, extending the result proved by the same authors in the case of Lipschitz continuous coefficients.