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

Abstract : 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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https://hal.archives-ouvertes.fr/hal-01981330
Contributor : Pierre Gilles Lemarié-Rieusset <>
Submitted on : Tuesday, January 15, 2019 - 12:51:40 AM
Last modification on : Tuesday, March 17, 2020 - 1:49:46 AM
Document(s) archivé(s) le : Tuesday, April 16, 2019 - 12:39:44 PM

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  • HAL Id : hal-01981330, version 1
  • ARXIV : 1901.05649

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Pierre Gilles Lemarié-Rieusset. Interpolation, extrapolation, Morrey spaces and local energy control for the Navier--Stokes equations.. 2019. ⟨hal-01981330⟩

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