An evidence of temporal discontinuity of the solution in \(F^s_{1, \infty }(\mathbb {R}^d)\) is presented, which implies the ill-posedness of the Cauchy problem for the Euler equations. Continuity and weak-type continuity of the solutions in related spaces are also discussed.

中文翻译：

---

端点临界 Triebel–Lizorkin 空间中不可压缩欧拉方程解的时间正则性 $$F^{d+1}_{1, \infty }(\mathbb {R}^d)$$

给出了\(F^s_{1, \infty }(\mathbb {R}^d)\)中解的时间不连续性的证据，这意味着欧拉方程的柯西问题的不适定性。还讨论了相关空间中解的连续性和弱型连续性。