The mathematical theory of the Navier-Stokes equations presents still fundamental open questions that represent as many challenges for the interested mathematicians. This volume collects a series of articles whose objective is to furnish new contributions and ideas to these questions, with particular regard to turbulence modelling, regularity of solutions to the initial-value problem, flow in region with an unbounded boundary and compressible flow. Contributors: A. Biryuk D. Chae and J. Lee A. Dunca, V. John and W.J. Layton T. Hishida T. Leonaviciene and K. Pileckas