Wiedemann, Emil Existence of weak solutions for the incompressible Euler equations. (English) Zbl 1228.35172 Ann. Inst. Henri Poincaré, Anal. Non Linéaire 28, No. 5, 727-730 (2011). Summary: Using a recent result of C. De Lellis and L. Székelyhidi jun. [Arch. Ration. Mech. Anal. 195, No. 1, 225–260 (2010; Zbl 1192.35138)] we show that, in the case of periodic boundary conditions and for arbitrary space dimension \(d \geq 2\), there exist infinitely many global weak solutions to the incompressible Euler equations with initial data \(v_0\), where \(v_0\) may be any solenoidal \(L^2\)-vector field. In addition, the energy of these solutions is bounded in time. Cited in 29 Documents MSC: 35Q31 Euler equations 76B03 Existence, uniqueness, and regularity theory for incompressible inviscid fluids Keywords:incompressible Euler equation PDF BibTeX XML Cite \textit{E. Wiedemann}, Ann. Inst. Henri Poincaré, Anal. Non Linéaire 28, No. 5, 727--730 (2011; Zbl 1228.35172) Full Text: DOI arXiv References: [1] Constantin, Peter; Foias, Ciprian, Navier-Stokes equations, Chicago lectures in math., (1988), The University of Chicago Press Chicago · Zbl 0687.35071 [2] De Lellis, Camillo; Székelyhidi, László, On admissibility criteria for weak solutions of the Euler equations, Arch. ration. mech. anal., 195, 1, 225-260, (2010) · Zbl 1192.35138 [3] Leray, Jean, Sur le mouvement dʼun liquide visqueux emplissant lʼespace, Acta math., 63, 1, 193-248, (1934) · JFM 60.0726.05 [4] Székelyhidi, László; Wiedemann, Emil, Generalised Young measures generated by ideal incompressible fluid flows, (2011), preprint: · Zbl 1256.35072 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.