Piecewise smooth stationary Euler flows with compact support via overdetermined boundary problems
Analysis of PDEs
2020-12-02 v1
Abstract
We construct new stationary weak solutions of the 3D Euler equation with compact support. The solutions, which are piecewise smooth and discontinuous across a surface, are axisymmetric with swirl. The range of solutions we find is different from, and larger than, the family of smooth stationary solutions recently obtained by Gavrilov and Constantin-La-Vicol; in particular, these solutions are not localizable. A key step in the proof is the construction of solutions to an overdetermined elliptic boundary value problem where one prescribes both Dirichlet and (nonconstant) Neumann data.
Cite
@article{arxiv.2005.04380,
title = {Piecewise smooth stationary Euler flows with compact support via overdetermined boundary problems},
author = {Miguel Domínguez-Vázquez and Alberto Enciso and Daniel Peralta-Salas},
journal= {arXiv preprint arXiv:2005.04380},
year = {2020}
}