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- W2963584986 abstract "We consider the system of (pure) gravity water waves in any dimension and in a fluid domain with a general bottom geometry. The unique solvability of this problem was established by Alazard–Burq–Zuily [Invent. Math. 198(1) (2014) 71–163] at a low regularity level where the initial surface is [Formula: see text] in terms of Sobolev embeddings; this result allows the existence of free surfaces with unbounded curvature. Our result states that the solutions obtained in the above work depend continuously on initial data in the strong topology in which the solutions are constructed. This establishes a well-posedness result in the sense of Hadamard." @default.
- W2963584986 created "2019-07-30" @default.
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- W2963584986 date "2016-12-01" @default.
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- W2963584986 title "Hadamard well-posedness of the gravity water waves system" @default.
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- W2963584986 doi "https://doi.org/10.1142/s0219891616500211" @default.
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