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This volume presents original papers reporting novel results that range from an experimental study on cavitation jets to up-to-date mathematical analysis of the Navier-Stokes equations for free boundary problems, reflecting features of the International Conference on Mathematical Fluid Dynamics, Present and Future, held 11-14 November 2014 at Waseda University in Tokyo. The contributions address subjects in one- and two-phase fluid flows including cavitation, liquid crystal flows, plasma flows, and blood flows. Written by internationally established experts, these papers highlight the connections between mathematical, experimental, and computational fluid dynamics. The volume addresses a large audience in mathematics and engineering, including researchers and graduate students interested in mathematical fluid dynamics.§