Well-Posedness for SDEs with Logarithmical Critical Distributional Drifts

We study the stochastic differential equation $$d X_t=b(t,X_t)d t+\sqrt{2}d W_t$$ on $\mathbb R^d$, where $b$ is a time-dependent, divergence-free distributional drift of critical Hölder--Besov regularity $-1$, strengthened by an iterated-logarithmic correction. For every initial probability law, we