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A counterexample to the smoothness of the solution to an equation arising in fluid mechanics. (English) Zbl 1090.35146

An equation arising from the Eulerian-Lagrangian description of incompressible fluid motion is analyzed. Known results in nonviscous flow are discussed in the viscous case. It is shown that the correspondence between the description in question can be invertible for a short time only. In this context, also global regularity for Navier-Stokes equations is discussed.

MSC:

35Q35 PDEs in connection with fluid mechanics
76D05 Navier-Stokes equations for incompressible viscous fluids
55M25 Degree, winding number
60H30 Applications of stochastic analysis (to PDEs, etc.)
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