Fabrice Planchon

On the regularity of the bilinear term for solutions to the incompressible Navier-Stokes equations

We derivevarious estimates for strong solutioms to the Navier-Stokes equations in C([O, T), L3(R3)) that allow us to prove some regularity results on the kinematic bilinear term.

STRONG SOLUTIONS TO THE INCOMPRESSIBLE NAVIER-STOKES EQUATIONS IN THE HALF-SPACE

We derive an exact formula for solutions to the Stokes equations in the half space with an external forcing term. This formula is used to establish local and global existence and uniqueness in a suitable Besov space for solutions to the Navier Stokes equations. In particular, wellposedness is proved for initial data in L3(R3 +).

Adaptive Gabor transforms

Abstract We aim to provide time-frequency representations of a one-dimensional signal where the window is locally adapted to the signal, thus providing a better readability of the representation.

The Benjamin—Ono equation in energy space

We prove existence of solutions for the Benjamin—Ono equation with data in H s(ℝ), s > 0. Thanks to conservation laws, this yields global solutions for H 1 2 (ℝ) data, which is the natural “finite energy” class. Moreover, unconditional uniqueness is obtained in L t ∞ (H 1 2 (ℝ)), which includes weak solutions, while for s > 3 20 , uniqueness holds in a suitable space.