The generalized Caffarelli-Kohn-Nirenberg Theorem for the hyperdissipative Navier-Stokes system

Abstract

We introduce a notion of suitable weak solution of the hyperdissipative Navier-Stokes equations and we achieve a corresponding extension of the regularity theory of Caffarelli-Kohn-Nirenberg.

References in corpus (4)

• An extension problem related to the fractional Laplacian
• On higher order extensions for the fractional Laplacian
• Global regularity for a slightly supercritical hyperdissipative Navier-Stokes system
• Partial regularity of suitable weak solutions to the multi-dimensional generalized magnetohydrodynamics equations

Cited by in corpus (8)

• The fractional $p$-biharmonic systems: optimal Poincaré constants, unique continuation and inverse problems
• Local regularity of weak solutions of the hypodissipative Navier-Stokes equations
• Partial regularity of Leray-Hopf weak solutions to the incompressible Navier-Stokes equations with hyperdissipation
• Phase transitions in the fractional three-dimensional Navier-Stokes equations
• Global Regularity of weak solutions to the generalized Leray equations and its applications
• Global existence of uniformly locally energy solutions for the incompressible fractional Navier-Stokes equations
• Global well-posedness for 2D fractional inhomogeneous Navier-Stokes equations with rough density
• Mild criticality breaking for the Navier-Stokes equations