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arXiv · 1901.05649

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

Pierre Gilles Lemarié-Rieusset
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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-H{\"o}lder 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 $\partial$ t u + u. $\nabla$ u = $\Delta$ u -- $\nabla$p div u = 0 u(0, .) = u 0 *

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Pierre Gilles Lemarié-Rieusset. 2019-01-17. Interpolation, extrapolation, Morrey spaces and local energy control for the Navier--Stokes equations. https://arxiv.org/abs/1901.05649

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