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

Montgomery-Smith, Stephen; Pokorný, Milan

Commentat. Math. Univ. Carol. 43, No. 1, 61-75 (2002).

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.

Reviewer: Ivan Straškraba (Praha)

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.)

Keywords:

Navier-Stokes equations; Euler equations; regularity of systems of PDE’s; Eulerian-Lagrangian description of viscous fluids