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On Kato’s conditions for vanishing viscosity. (English) Zbl 1125.76014

The author proves that Kato’s condition under which the vanishing viscosity limit of a sufficiently smooth solution of Navier-Stokes equations is a solution of Euler equations, involving the gradient of velocity, may be rephrazed into a similar condition involving the vorticity.

MSC:

76D03 Existence, uniqueness, and regularity theory for incompressible viscous fluids
76B03 Existence, uniqueness, and regularity theory for incompressible inviscid fluids
35Q30 Navier-Stokes equations
35Q35 PDEs in connection with fluid mechanics
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