A variable-step second-order ETD-mr-SAV scheme for the periodic NSE is claimed to be uniformly long-time stable, but the proof's key sum bound is erroneous and second-order accuracy is only argued heuristically.
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Unconditionally Long-Time Stable Variable-Step Second-Order ETD Schemes for the 2D Periodic Incompressible NSE
A variable-step second-order ETD-mr-SAV scheme for the periodic NSE is claimed to be uniformly long-time stable, but the proof's key sum bound is erroneous and second-order accuracy is only argued heuristically.