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(In)finite extent of stationary perfect fluids in Newtonian theory. (English) Zbl 1362.76008

Summary: For stationary, barotropic fluids in Newtonian gravity we give simple criteria on the equation of state and the “law of motion” which guarantee finite or infinite extent of the fluid region (providing a priori estimates for the corresponding stationary Newton-Euler system). Under more restrictive conditions, we can also exclude the presence of “hollow” configurations. Our main result, which does not assume axial symmetry, uses the virial theorem as the key ingredient and generalises a known result in the static case. In the axially symmetric case stronger results are obtained and examples are discussed.

MSC:

76B03 Existence, uniqueness, and regularity theory for incompressible inviscid fluids
35Q35 PDEs in connection with fluid mechanics
85A05 Galactic and stellar dynamics
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