Kinetic SDEs dX=V dt, dV=b dt+sqrt(2)dW with distributional drift b of anisotropic Holder order alpha in (-1,0) and bounded velocity divergence admit unique weak solutions, with Krylov and moment estimates.
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Kinetic SDEs with subcritical distributional drifts
Kinetic SDEs dX=V dt, dV=b dt+sqrt(2)dW with distributional drift b of anisotropic Holder order alpha in (-1,0) and bounded velocity divergence admit unique weak solutions, with Krylov and moment estimates.