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This paper is devoted to the existence of conformal metrics on with prescribed scalar curvature. We extend well known existence criteria due to Bahri-Coron.
For a bounded domain , we use the notion of very weak solutions to obtain a new and large uniqueness class for solutions of the inhomogeneous Navier-Stokes system , , with , , and very general data classes for , , such that may have no differentiability property. For smooth data we get a large class of unique and regular solutions extending well known classical solution classes, and generalizing regularity results. Moreover, our results are closely related to those of a series of...
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