Abstract
We use a convex integration construction from [22] in a Baire category argument to show that weak solutions to the transport equation with incompressible vector fields with Sobolev regularity are generic in the Baire category sense. Using the construction of [7] we prove an analog statement for the 3D Navier–Stokes equations.
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G. S. thanks Luigi de Rosa for useful discussionson the topic of this paper.
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This work was supported by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No. 724298-DIFFINCL).
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Sattig, G., Székelyhidi, L. The Baire category method for intermittent convex integration. Acta Math. Hungar. 171, 88–106 (2023). https://doi.org/10.1007/s10474-023-01380-0
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DOI: https://doi.org/10.1007/s10474-023-01380-0