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On the smoothness of trajectories in incompressible perfect fluids. (English) Zbl 0972.35102
Guo, Yan (ed.), Nonlinear wave equations. A conference on honor of Walter A. Strauss on the occasion of his sixtieth birthday, Brown University, Providence, RI, USA, May 2-3, 1998. Providence, RI: American Mathematical Society (AMS). Contemp. Math. 263, 109-130 (2000).
After revising all proofs available in the literatures, the author gives a new proof that, under reasonable assumptions, the trajectory of a fluid particle in the Euler flow of incompressible perfect fluid is infinitely smooth in time. The proof uses the modern analysis on manifolds.
For the entire collection see [Zbl 0947.00025].

MSC:
35Q35 PDEs in connection with fluid mechanics
76B03 Existence, uniqueness, and regularity theory for incompressible inviscid fluids
35R35 Free boundary problems for PDEs
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