• Corpus ID: 248506058

Geometric Hydrodynamics in Open Problems

  title={Geometric Hydrodynamics in Open Problems},
  author={Boris Khesin and Gerard Misiołek and Alexander Shnirelman},
Geometric Hydrodynamics has flourished ever since the celebrated 1966 paper of V. Arnold. In this paper we present a collection of open problems along with several new constructions in fluid dynamics and a concise survey of recent developments and achievements in this area. The topics discussed include variational settings for different types of fluids, models for invariant metrics, the Cauchy and boundary value problems, partial analyticity of solutions to the Euler equations, their steady and… 

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  • K. KhaninA. Sobolevski
  • Mathematics
    Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
  • 2010
It is shown that, for any convex Hamiltonian, there exists a uniquely defined canonical global non-smooth coalescing flow that extends particle trajectories and determines the dynamics inside shocks.