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])
L2-density of wild initial data for the hypodissipative Navier-Stokes equations
Gorini, Michele
2023-01-01
Abstract
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])File in questo prodotto:
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