Well-posedness of the 2D Euler equations when velocity grows at infinity. (English) Zbl 1412.35237
Summary: We prove the uniqueness and finite-time existence of bounded-vorticity solutions to the 2D Euler equations having velocity growing slower than the square root of the distance from the origin, obtaining global existence for more slowly growing velocity fields. We also establish continuous dependence on initial data.
MSC:
| 35Q31 | Euler equations |
| 76B03 | Existence, uniqueness, and regularity theory for incompressible inviscid fluids |
| 35A01 | Existence problems for PDEs: global existence, local existence, non-existence |
| 35A02 | Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness |
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