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SDEs with critical general distributional drifts: sharp solvability and blow ups
D. Kinzebulatov, R. Vafadar
https://arxiv.org/abs/2506.09244 https://

SDEs with critical general distributional drifts: sharp solvability and blow ups
We establish weak well-posedness for SDEs having discontinuous diffusion coefficients and general distributional drifts that may introduce blow up effects. Our drifts satisfy minimal assumptions, i.e.\,we assume only that the Cauchy problem for the Kolmogorov backward equation is well-posed in the standard Hilbert triple $W^{1,2} \hookrightarrow L^2 \hookrightarrow W^{-1,2}$. By a result of Mazya and Verbitsky, these assumptions are precisely those drifts that can be represented as the sum of a…