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Ill-posedness issue on the Oldroyd-B model in the critical Besov spaces (2403.02001v2)
Published 4 Mar 2024 in math.AP
Abstract: It is proved in \cite[J. Funct. Anal., 2020]{AP} that the Cauchy problem for some Oldroyd-B model is well-posed in $\B{d/p-1}_{p,1}(\Rd) \times \B{d/p}_{p,1}(\Rd)$ with $1\leq p<2d$. In this paper, we prove that the Cauchy problem for the same Oldroyd-B model is ill-posed in $\B{d/p-1}_{p,r}(\Rd) \times \B{d/p}_{p,r}(\Rd)$ with $1\leq p\leq \infty$ and $1< r\leq\infty$ due to the lack of continuous dependence of the solution.