The reduced 2D Kuramoto-Sivashinsky model (1.4) is claimed to be globally well-posed for H1 initial data with the first component in L∞, but the proof's final Gronwall step does not go through as written.
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On the well-posedness of an anisotropically-reduced two-dimensional Kuramoto-Sivashinsky equation
The reduced 2D Kuramoto-Sivashinsky model (1.4) is claimed to be globally well-posed for H1 initial data with the first component in L∞, but the proof's final Gronwall step does not go through as written.