Domínguez Vázquez, MiguelEnciso, AlbertoPeralta-Salas, Daniel2024-10-042024-10-042021Domínguez-Vázquez, M., Enciso, A. & Peralta-Salas, D. Piecewise Smooth Stationary Euler Flows with Compact Support Via Overdetermined Boundary Problems. Arch Rational Mech Anal 239, 1327–1347 (2021). https://doi.org/10.1007/s00205-020-01594-4http://hdl.handle.net/10347/35015This version of the article has been accepted for publication, after peer review (when applicable) and is subject to Springer Nature’s AM terms of use, but is not the Version of Record and does not reflect post-acceptance improvements, or any corrections. The Version of Record is available online at: http://dx.doi.org/10.1007/s00205-020-01594-4We 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.engjournal article10.1007/s00205-020-01594-4open access