Stochastic turbulence for Burgers equation driven by cylindrical Lévy process

The paper proves, for 1D viscous Burgers on the torus with additive cylindrical Lévy forcing (bounded jumps, space-smooth coefficients βk ≍ λk^{-γ0}, γ0>1), the bifractal structure-function law and k^{-2} layer-averaged energy spectrum in the same inertial/dissipation ranges as in the Gaussian case. It builds on: (i) well-posedness and mass conservation, (ii) Lévy–Itô energy identities and ν-uniform time–ensemble Sobolev bounds ⟨⟨‖u‖_{H^n}^{2n}⟩⟩ ≍ ν^{-(2n−1)} and ⟨⟨‖∂xu‖_2^2⟩⟩ ≍ ν^{-1}, (iii) Oleinik–Kruzhkov one-sided bounds to control upslopes, and (iv) the usual Parseval/shell-averaging step for the spectrum. The candidate model solution follows the same four-step route and matches the statements and scalings proved in the paper; any differences are not substantive.