Table of contents

Lecture notes : Mathematical study of singular perturbation problems Applications to large-scale oceanography

Talk no. 1, 49 p.
Around Nash inequalities

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Talk no. 2, 16 p.
Whitham averaged equations and modulational stability of periodic traveling waves of a hyperbolic-parabolic balance law

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Talk no. 3, 24 p.
Cauchy problem for hyperbolic operators with triple characteristics of variable multiplicity

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Talk no. 4, 13 p.
Some recent results on the Muskat problem

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Talk no. 5, 14 p.
Hyperbolic equations and SBV functions

Talk no. 6, 10 p.
Electromagnetic Schrödinger flow: multiplier methods for dispersion

Talk no. 7, 13 p.
Space-time resonances

Talk no. 8, 10 p.
Hypoelliptic estimates for some linear diffusive kinetic equations

Talk no. 9, 13 p.
Energy Critical nonlinear Schrödinger equations in the presence of periodic geodesics

Talk no. 10, 10 p.
Dispersive and Strichartz estimates for the wave equation in domains with boundary

Talk no. 11, 19 p.
Profile decompositions and applications to Navier-Stokes

Talk no. 12, 13 p.
Carleman estimates for elliptic operators with jumps at an interface: Anisotropic case and sharp geometric conditions

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Talk no. 13, 23 p.
Traveling waves for nonlinear Schrödinger equations with nonzero conditions at infinity: some results and open problems

Talk no. 14, 22 p.
Entropy of eigenfunctions of the Laplacian in dimension 2

Talk no. 15, 17 p.