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Chae and Wolf recently constructed discretely self-similar solutions to theNavier-Stokes equations for any discretely self similar data in$L^2_{\mathrm{loc}}$. Their solutions are in the class of local Leray solutionswith projected pressure, and satisfy the "local energy inequality withprojected pressure". In this note, for the same class of initial data, weconstruct discretely self-similar suitable weak solutions to the Navier-Stokesequations that satisfy the classical local energy inequality of Scheffer andCaffarelli-Kohn-Nirenberg. We also obtain an explicit formula for the pressurein terms of the velocity. Our argument involves a new purely local energyestimate for discretely self-similar solutions with data in$L^2_{\mathrm{loc}}$ and an approximation of divergence free, discretelyself-similar vector fields in $L^2_{\mathrm{loc}}$ by divergence free,discretely self-similar elements of $L^3_w$.

Discretely self-similar solutions to the Navier-Stokes equations with data in $L^2_{\mathrm{loc}}$ satisfying the local energy inequality