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3

You have to define what a soliton is. The most accepted definition in field theory is that a soliton is a stable, localized and finite energy/energy density solution of the equations of motions of the theory. A vortex ring is localized in space, it has finite energy and definitely is the solution of some equation of motion. Then if it is stable, it can ...

1

If by rotational flow you mean $$\vec{\omega} := \nabla \times \vec{u} \ne 0$$ everywhere, then the answer to your question is Yes, vorticity can be introduced through the fluid boundaries (see Klein's Kafeeloffel experiment) No, conservation of total vorticity means any vorticity in the fluid stays with the fluid (unless there is a vorticity sink ...

0

1) Yes. The rotational flow of a rigidly rotating fluid (in a rotating cylinder, for example) is a perfectly good solution of the Euler equation. 2) No. For one, the rigidly rotating flow described in 1) is perfectly stable, even if viscosity is taken into account. Furthermore, the main phenomenon described by the Navier-Stokes equation is vorticity ...

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