Enhanced Dissipation under Variable Growth: Stochastic $p(x)$-Laplace Equations with Transport Noise

We study dissipation enhancement for stochastic $p(x)$-Laplace equations with divergence-free transport noise on $\mathbb T^d$, $d\ge2$. Under log-Hölder continuity and degenerate subcritical growth, we establish global variational well-posedness and an exact energy identity. For every prescribed po