We prove global existence of weak solutions for the co-rotational FENE dumbbell model and the Doi model also called the Rod model. The proof is based on propagation of compactness, namely if we takeâ€¦ (More)

We prove local and global well-posedness for the FENE dumbbell model for a very general class of potentials. Indeed, in prior local or global well-posedness results conditions on the parameter b wereâ€¦ (More)

We show existence of global solutions for the gravity water waves equation in dimension 3, in the case of small data. The proof combines energy estimates, which yield control of L related norms, withâ€¦ (More)

This chapter is devoted to the study of some asymptotic problems in hydrodynamics. In particular, we will review results about the inviscid limit, the compressible-incompressible limit, the study ofâ€¦ (More)

We prove existence and uniqueness of solutions to the Klein-Gordon-Zakharov system in the energy space H Ã— L on some time interval which is uniform with respect to two large parameters c and Î±. Theseâ€¦ (More)

We prove existence and uniqueness of local and global solutions for a system of equations concerning an incompressible viscoelastic fluid of the Oldroyd type. We also show a new a priori estimate forâ€¦ (More)

â€“ We prove some asymptotic results concerning global (weak) solutions of compressible isentropic Navierâ€“Stokes equations. More precisely, we establish the convergence towards solutions ofâ€¦ (More)

In this paper we prove two results about the inviscid limit of the NavierStokes system. The first one concerns the convergence in H of a sequence of solutions to the Navier-Stokes system when theâ€¦ (More)

We prove that there exists an interval of time which is uniform in the vanishing viscosity limit and for which the Navier-Stokes equation with Navier boundary condition has a strong solution. Thisâ€¦ (More)

This paper concerns the ergodic theory of a class of nonlinear dissipative PDEs of parabolic type. Leaving precise statements for later, we first give an indication of the nature of our results. Weâ€¦ (More)