Abstract
This paper concerns the compressible Navier–Stokes–Korteweg equations. Based on previous work [Li et al., Arch. Ration. Mech. Anal. 232, 557–590 (2019)], we prove that the classical solution with finite energy does not exist in the inhomogeneous Sobolev space for any short time under some natural assumptions on initial data near the vacuum.
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