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Incompressible viscous flows in borderline Besov spaces. (English) Zbl 1147.76014
Summary: We establish two new estimates for a transport-diffusion equation. As an application, we treat the problem of global persistence of Besov regularity \(B_{p,1}^{\frac{2}{p}+1},\) with \(p \in ]2,+\infty]\) , for the two-dimensional Navier-Stokes equations with uniform bounds on viscosity. We provide also an inviscid global result.

MSC:
76D03 Existence, uniqueness, and regularity theory for incompressible viscous fluids
35Q30 Navier-Stokes equations
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