Energy Solutions and Harnack Estimates for Nonlocal Drift–Diffusion
Source: hexagonmath.org/abs/2611.00047v1
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…
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