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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. BiryukD. Chae and J. LeeA. Dunca, V. John and W.J. LaytonT. HishidaT. Leonaviciene and K. Pileckas