Hydrodynamics is a large area of Mathematics that has many interdisciplinary connections and comprises many different sub-fields. It revolves around classical sets of problems in Analysis and Applied Mathematics, and it has been an area of major recent advances. The problems principally involve the study of nonlinear partial differential equations (PDEs) that describe fluid motion in various physical settings. The most prominent examples are the Euler and Navier-Stokes equations, which were already introduced in the 18th century. They have attracted the attention of countless researchers and still remain at the center of some of the most important open scientic questions, such as the "theory of turbulence" and the Clay Millenium problem on the regularity of the Navier-Stokes equations. Other topics of enduring interest include equations for water waves, and the large number of questions connected to fluid dynamics and collective motion in biological settings.

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