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- W3048757470 abstract "We show that for any given solenoidal initial data in $L^2$ and any solenoidal external force in $L_{text{loc}}^q bigcap L^{3/2}$ with $q>3$, there exist partially regular weak solutions of the Navier-Stokes equations in $R^4 times [0,infty[$ which satisfy certain local energy inequalities and whose singular sets have locally finite $2$-dimensional parabolic Hausdorff measure. With the help of a parabolic concentration-compactness theorem we are able to overcome the possible lack of compactness arising in the spatially $4$-dimensional setting by using defect measures, which we then incorporate into the partial regularity theory." @default.
- W3048757470 created "2020-08-18" @default.
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- W3048757470 date "2021-01-12" @default.
- W3048757470 modified "2023-09-23" @default.
- W3048757470 title "Partially Regular Weak Solutions of the Navier–Stokes Equations in $$mathbb {R}^4 times [0,infty [$$" @default.
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- W3048757470 doi "https://doi.org/10.1007/s00205-020-01603-6" @default.
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