Incompressible viscous flows in borderline Besov spaces

Taoufik Hmidi (1) , Sahbi Keraani (1)

1 IRMAR - Institut de Recherche Mathématique de Rennes

We establish two new estimates for a transport-diffusion equation. As an application we treat the problem of global persistence of the Besov regularity $B_{p, 1}^{2/p+1}$, with $p\in ]2,+\infty]$, for the two-dimensional Navier-Stokes equations with uniform bounds on the viscosity. We provide also an inviscid global result.

Mots clés: NAVIER-STOKES SYSTEM; EULER EQUATIONS; EXISTENCE

Domaines: Equations aux dérivées partielles [math.AP]

Taoufik Hmidi, Sahbi Keraani. Incompressible viscous flows in borderline Besov spaces. Archive for Rational Mechanics and Analysis, 2008, 189 (2), pp.283-300. ⟨10.1007/s00205-008-0115-7⟩. ⟨hal-00360590⟩