On the uniqueness of weak solutions for the 3D Navier-Stokes equations

Abdelhafid Younsi (1)

1 LAMNEDP - Laboratoire d'Analyse Mathématique et Numérique des Equations aux Dérivées Partielles

We investigate general topology properties to show that the set of solutions of the Navier-Stokes is homeomorphic to the set of solutions of regularized Navier-Stokes equations by adding a high-order viscosity term. This result means that the set of solutions is reduced to one solution for each dimension d<=4. We also prove a high regularity for solution to the Navier-Stokes equations.

Mots clés: hyperviscosity

Mots clés: hyperviscosity.; Navier-Stokes equations; solution uniqueness; weak Leray-Hopf solution

Domaines: Equations aux dérivées partielles [math.AP]

Abdelhafid Younsi. On the uniqueness of weak solutions for the 3D Navier-Stokes equations. 2011. ⟨hal-00586485v2⟩