Kato, Tosio 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]. Reviewer: Oleg Titow (Berlin) Cited in 8 Documents MSC: 35Q35 PDEs in connection with fluid mechanics 76B03 Existence, uniqueness, and regularity theory for incompressible inviscid fluids 35R35 Free boundary problems for PDEs Keywords:infinite smoothness in time; trajectory of fluid particle; Euler flow; incompressible perfect fluid PDFBibTeX XMLCite \textit{T. Kato}, Contemp. Math. 263, 109--130 (2000; Zbl 0972.35102)