Non-linear analysis method and application to fluid mechanics

Fourier analysis methods and applications: Littlewood-Paley decomposition, para-products and para-linearization, functional spaces. – Incompressible fluids: Anisotropic Navier-Stokes system, Global Regularity for the Navier-Stokes system for some class of large solutions, Hydrostatic approximation of the Navier-Stokes system in a the strip, Global solutions for the Prandtl equation with small analytic data. Hyperbolic Navier-Stokes system. Density dependent Navier-Stokes system. – Compressible fluids: Dispersifs effects for the compressible Euler system, Rough solutions for the compressible Navier-Stokes system and the compressible Navier-Stokes system with capillarity.