Non-uniqueness and h-principle for Hölder-continuous weak solutions of the Euler equations - Daneri, Sara; Székelyhidi Jr., László (2016)
In this paper we address the Cauchy problem for the incompressible Euler equations in the periodic setting. Based on estimates developed in [Buckmaster-De Lellis-Isett-Sz'ekelyhidi], we prove that the set of H"older 15- wild initial data is dense in L2, where we call an initial datum wild if it admits infinitely many admissible H"older 15- weak solutions. We also introduce a new set of stationary flows which we use as a perturbation profile instead of Beltrami flows to recover arbitrary Reynolds stresses.