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A constructive approach to regularity of Lagrangian trajectories for incompressible Euler flow in a bounded domain. (English) Zbl 1371.35201

This paper studies the regularity of Lagrangian trajectories for incompressible Euler flow in a bounded domain. A constructive approach, which use the Cauchy’s Lagrangian formulation, was posed to discuss the regularity of Lagrangian trajectories for incompressible Euler flows without boundaries. The main goal of this paper is to extend this constructive method to Euler flow with a boundary, and show that the smoothness of the Lagrangian characteristic curves for the incompressible Euler flow in a bounded domain is only limited by the smoothness of the domain boundary.
Reviewer: Cheng He (Beijing)

MSC:

35Q31 Euler equations
35B65 Smoothness and regularity of solutions to PDEs
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