- Journal Article
We show that for any given solenoidal initial data in L-2 and any solenoidal external force in L-loc(q) boolean AND L-3/2 with q > 3, there exist partially regular weak solutions of the Navier-Stokes equations in R-4 x [0, infinity[ which satisfy certain local energy inequalities and whose singular sets have a locally finite 2-dimensional parabolic Hausdorff measure. With the help of a parabolic concentration-compactness theoremwe 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. Show more
Journal / seriesArchive for Rational Mechanics and Analysis
Pages / Article No.
Organisational unit03239 - Struwe, Michael (emeritus) / Struwe, Michael (emeritus)
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