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This volume contains the proceedings of the International Conference on Vorticity, Rotation and Symmetry (IV)--Complex Fluids and the Issue of Regularity, held from May 8-12, 2017, in Luminy, Marseille, France. The papers cover topics in mathematical fluid mechanics ranging from the classical regularity issue for solutions of the 3D Navier-Stokes system to compressible and non-Newtonian fluids, MHD flows and mixtures of fluids; discussing topics of different kinds of solutions, boundary conditions, and interfaces.

In recent years, the Fourier analysis methods have expereinced a growing interest in the study of partial differential equations. In particular, those techniques based on the Littlewood-Paley decomposition have proved to be very efficient for the study of evolution equations. The present book aims at presenting self-contained, state- of- the- art models of those techniques with applications to different classes of partial differential equations: transport, heat, wave and Schrodinger equations. It also offers more sophisticated models originating from fluid mechanics (in particular the...