It is proved in [J. Funct. Anal., 2020]{AP} that the Cauchy problem for some Oldroyd-B model is well-posed in d/p-1p,1(ᵈ) × d/pp,1(ᵈ) with 1≤ p<2d. In this paper, we prove that the Cauchy problem for the same Oldroyd-B model is ill-posed in d/p-1p,r(ᵈ) × d/pp,r(ᵈ) with 1≤ p≤ ∞ and 1< r≤∞ due to the lack of continuous dependence of the solution.
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Li et al. (2024) studied this question.
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