Abstract:
The key unsolved problems of mathematical fluid dynamics, their current state and outlook are discussed. These problems concern global existence and uniquness theorems for basic boundary and initial-boundary value problems in the theory of ideal and viscous incompressible fluids, the spectral problems in hydrodynamic stability theory for steady and time periodic flows, creation of secondary, tertiary, etc…flow regimes as a result of bifurcations and the asymptotics of vanishing viscosity. Several new problems are formulated.
Key words and phrases:Incompressible fluid, unsolved problems, existence, uniqueness, stability, asymptotics.
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