Discrete Gevrey Smoothing for Finite-Difference Heat and Navier–Stokes Operators: Sharp Constants and Analyticity Radius Estimates

Key Points

• The aim is to investigate the discrete analogue of the finite-difference Laplacian and its properties.
• Analyzed the finite-difference heat operators and Navier-Stokes equations.
• Applied discrete Gevrey smoothing techniques to assess analyticity.
• Employed mathematical proofs to establish bounds and estimates.
• Confirmed that discrete Navier-Stokes solutions exhibit strongly analytic behavior.
• Established sharp constants for the smoothing properties associated with finite-difference operators.
• Estimated the analyticity radius for the discrete settings, providing new insights.