L2-density of wild initial data for the hypodissipative Navier-Stokes equations

摘要

© 2022 Elsevier Inc.In this paper we deal with the Cauchy problem for the hypodissipative Navier-Stokes equations in the three-dimensional periodic setting. For all Laplacian exponents [Formula presented], we prove non-uniqueness of dissipative Lt2Hxθ weak solutions for an L2-dense set of Cβ Hölder continuous wild initial data with [Formula presented]. This improves previous results of non-uniqueness for infinitely many wild initial data ([8,20]) and generalizes previous results on density of wild initial data obtained for the Euler equations ([14,13]).