Strichartz Estimates and the Cauchy Problem for the Gravity Water Waves Equations
This memoir is devoted to the proof of a well-posedness result for the gravity water waves equations, in arbitrary dimension and in fluid domains with general bottoms, when the initial velocity field is not necessarily Lipschitz. Moreover, for two-dimensional waves, the authors consider solutions su...
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| Main Author: | |
| Other Authors: | , |
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Providence :
American Mathematical Society,
2019
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| Series: | Memoirs of the American Mathematical Society Ser.
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| Subjects: | |
| Local Note: | ProQuest Ebook Central |
| Summary: | This memoir is devoted to the proof of a well-posedness result for the gravity water waves equations, in arbitrary dimension and in fluid domains with general bottoms, when the initial velocity field is not necessarily Lipschitz. Moreover, for two-dimensional waves, the authors consider solutions such that the curvature of the initial free surface does not belong to L^2. The proof is entirely based on the Eulerian formulation of the water waves equations, using microlocal analysis to obtain sharp Sobolev and Hölder estimates. The authors first prove tame estimates in Sobolev spaces depending l. |
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| Physical Description: | 1 online resource (120 pages) |
| ISBN: | 9781470449216 1470449218 |
| Source of Description, Etc. Note: | Print version record. |
