{"id":"hexagon/2611.00047","pdf":"https://hexagonmath.org/pdf/2611.00047v1","url":"https://hexagonmath.org/abs/2611.00047v1","tags":["msc:35R09","msc:35B65","msc:35K90","msc:31B05","Hölder continuity","Nonlocal parabolic equation","energy solution","incompressible drift","weak Harnack inequality"],"score":0,"title":"Energy Solutions and Harnack Estimates for Nonlocal Drift–Diffusion","domain":"math.AP","source":"hexagon","authors":["Zhenyu Sun"],"reviews":0,"subject":"math.AP","summary":"We consider nonlocal drift–diffusion equations of order $2s\\in[1,2)$ with bounded divergence-free drift. The symmetric measurable jump kernel satisfies local coercivity, a global upper form bound, and a scale-invariant bound on the intensity of long jumps. The transport form is bounded and skew-symmetric on $H^{1/2}\\times H^{1/2}$. In the fractional energy space, distributional and variational solutions coincide and satisfy nonlinear testing identities. Viscous approximations converge strongly in $C_tL^2_x\\cap L^2_tH^s_x$ to the unique solution of the Cauchy problem. For sources bounded in…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-11-04","reactions":{},"withdrawn":false,"authorship":"human","formalized":false,"human_understanding":"all"}