We discuss existence and uniqueness of solutions to the Euler Equation in an unbounded domain of the plane. We only assume the vorticity to be bounded, whereas in this kind of problems assumptions on its decreasing at infinity are usually made. The solution is obtained as limit of solutions to problems with compactly supported data. The existence of such limit physically means that the effects of far away fluid particles on the local evolution is negligible.
Caprino, S., Marchioro, C. (2010). On the Euler equation in an unbounded domain of the plane. JOURNAL OF MATHEMATICAL FLUID MECHANICS, 12(1), 151-169 [10.1007/s00021-008-0279-9].
On the Euler equation in an unbounded domain of the plane
CAPRINO, SILVIA;
2010-01-01
Abstract
We discuss existence and uniqueness of solutions to the Euler Equation in an unbounded domain of the plane. We only assume the vorticity to be bounded, whereas in this kind of problems assumptions on its decreasing at infinity are usually made. The solution is obtained as limit of solutions to problems with compactly supported data. The existence of such limit physically means that the effects of far away fluid particles on the local evolution is negligible.File in questo prodotto:
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