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- W2160116649 abstract "We study weak solutions of the 3D Navier-Stokes equations in whole space with L 2 initial data. It will be proved that r u is locally integrable in space-time for any real such that 1 < < 3, which says that almost third derivative is locally integrable. Up to now, only second derivativer 2 u has been known to be locally integrable by standard parabolic regularization. We also present sharp estimates of those quantities in weak-L 4=( +1) loc . These estimates depend only on the L 2 norm of initial data and integrating domains. Moreover, they are valid even for 3 as long as u is smooth. The proof uses a good approximation of Navier-Stokes and a blow-up technique, which let us to focusing on a local study. For the local study, we use De Giorgi method with a new pressure decomposition. To handle non-locality of the fractional Laplacian, we will adopt some properties of the Hardy space and Maximal functions." @default.
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- W2160116649 date "2014-10-01" @default.
- W2160116649 modified "2023-09-30" @default.
- W2160116649 title "Estimates on fractional higher derivatives of weak solutions for the Navier–Stokes equations" @default.
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- W2160116649 doi "https://doi.org/10.1016/j.anihpc.2013.08.001" @default.
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