Gradient flow approach to Landau equation: A cross-product structure

We introduce a cross-product Landau gradient that commutes with Gaussian mollification. For the hard-potential interaction kernels of the form $A(|v-v_*|)\sim \langle v-v_*\rangle^γ|v-v_*|^2$ with $γ\in(-\infty,1]$, this construction yields a variational characterisation of the gradient-flow structu