This paper demonstrates ill-posedness in Cauchy problems for the Oldroyd-B model, highlighting implications for analysis.
It was proved in [11, J. Funct. Anal., 2020] that the Cauchy problem for some Oldroyd-B model is well-posed in Ḃd/p-1p,1(Rᵈ) × Ḃd/pp,1(Rᵈ) with 1≤ p < 2d . In this paper, we prove that the Cauchy problem for the same Oldroyd-B model is ill-posed in Ḃd/p-1p,r(Rᵈ) × Ḃd/pp,r(Rᵈ) with 1≤ p≤ ∞ and 1 < r≤∞ due to the lack of continuous dependence of the solution.
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Li et al. (2025) studied this question.
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