Global well posedness for the 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 sulutions is reduced to one slution for each dimension d≤4. We also prove a high regulariy of solution navier-Stokes equations.

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

Mots clés: hyperviscosity

Domaines: Equations aux dérivées partielles [math.AP]

Abdelhafid Younsi. Global well posedness for the Navier-Stokes equations. 2011. ⟨hal-00586485v1⟩