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])
2023
Convex integration; Hypodissipative Navier-Stokes equations; Wild initial data
File in questo prodotto:
File Dimensione Formato  
2023_JFunctAnal_284_109819_Gorini.pdf

non disponibili

Tipologia: Versione Editoriale (PDF)
Licenza: Non pubblico
Dimensione 1.1 MB
Formato Adobe PDF
1.1 MB Adobe PDF   Visualizza/Apri   Richiedi una copia

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.12571/34644
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 1
  • ???jsp.display-item.citation.isi??? 1
social impact