Adrien Tendani-Soler

The main focus of my research is to exhibit and quantify the smoothing effects for PDEs arising from fluid mechanics. More specifically, I aim to determine whether solutions are real analytic or holomorphic, and to quantify this regularity by estimating the domaine of analyticity using methods from Fourier analysis, harmonic analysis, pseudo-differential calculus or complex analysis. Beside, during my thesis, I have had the opportunity to develop this issue in various contexts, such as the analytic smoothing effects for some PDEs or to determine the reachable spaces in control theory. Furthermore, I have also worked on controllability for compressible fluid systems, using Carleman inequalities and duality methods, as well as on the well-posedness of certain PDEs in different types of functional spaces (spaces of pseudo-measures, Sobolev spaces associated with hypoelliptic operators, anisotropic Besov spaces) mainly through Fourier analysis techniques, propagation of vector fields, harmonic analysis on Lie groups, and anisotropic para-differential calculus.