On the regularity of the trajectories of a perfect fluid. (Régularité de la trajectoire des particules d’un fluide parfait incompressible remplissant l’espace.) (French) Zbl 0833.35112

Chemin, J.-Y.

J. Math. Pures Appl., IX. Sér. 71, No. 5, 407-417 (1992).

Summary: The goal of this paper is the proof of the fact that the integral curves of an enough regular vector field solution of the incompressible Euler system are smooth. The method used in this work is the study of the repeated action of a non smooth vector on a certain type of singular integral operators.

MSC:

35Q35	PDEs in connection with fluid mechanics
35L60	First-order nonlinear hyperbolic equations
76A02	Foundations of fluid mechanics

Keywords:

incompressible Euler system; singular integral operators