Local well-posedness of the viscous surface wave problem without surface tension

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Almost Exponential Decay of Periodic Viscous Surface Waves without Surface Tension (2013, unknown): “Then for any ε ∈ (0, 1) it holds that (5.42) ∂t (∥∥∥∂jt (χ2u)∥∥∥2 0 ) + ∥∥∥D∂jt (χ1u)∥∥∥2 0 .”
On the Cauchy problem for gravity water waves (2012, methodology): “Several extensions of their results have been obtained by different methods (see [22, 31, 32, 33, 35, 41, 54, 55, 59] for recent results and the surveys [11, 29, 36] for more references).”