Abstract.
We show some new uniqueness results for compressible flows with data having critical regularity. In the barotropic case, uniqueness is stated whenever the space dimension N satisfies N ≥ 2, and in the polytropic case, whenever N ≥ 3. The endpoints N = 2 in the barotropic case and N = 3 in the polytropic case were left open in [4], [5] and [6].
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Danchin, R. On the uniqueness in critical spaces for compressible Navier-Stokes equations. Nonlinear differ. equ. appl. 12, 111–128 (2005). https://doi.org/10.1007/s00030-004-2032-2
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DOI: https://doi.org/10.1007/s00030-004-2032-2