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Article Dans Une Revue Banach Center Publications Année : 2019

Interpolation, extrapolation, Morrey spaces and local energy control for the Navier--Stokes equations.

Résumé

Barker recently proved new weak-strong uniqueness results for the Navier-Stokes equations based on a criterion involving Besov spaces and a proof through interpolation between Besov-Hölder spaces and L 2. We improve slightly his results by considering Besov-Morrey spaces and interpolation between Besov-Morrey spaces and L 2 uloc. Let u 0 a divergence-free vector field on R 3. We shall consider weak solutions to the Cauchy initial value problem for the Navier-Stokes equations which satisfy energy estimates. The differential Navier-Stokes equations read as ∂ t u + u. ∇ u = ∆ u − ∇p div u = 0 u(0, .) = u 0 *
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Dates et versions

hal-01981330 , version 1 (15-01-2019)

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Pierre Gilles Lemarié-Rieusset. Interpolation, extrapolation, Morrey spaces and local energy control for the Navier--Stokes equations.. Banach Center Publications, 2019, 119, pp.279-294. ⟨10.4064/bc119-16⟩. ⟨hal-01981330⟩
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