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.
On the Euler Equation in an Unbounded Domain of the Plane / S., Caprino; Marchioro, Carlo. - In: JOURNAL OF MATHEMATICAL FLUID MECHANICS. - ISSN 1422-6928. - STAMPA. - 12:1(2010), pp. 151-169. [10.1007/s00021-008-0279-9]
On the Euler Equation in an Unbounded Domain of the Plane
MARCHIORO, Carlo
2010
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
