Abstract
In this survey article, we present results from the last several decades on several systems of PDE that model water waves. Some of those results provide short-time existence of smooth solutions; other results establish existence of smooth solutions for all time; still other results assert that singularities form in finite time.
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Acknowledgements
We thank Tania Pernas for providing the figures of the paper. DC was partially supported by the grants MTM2014-59488-P (Spain) and SEV-2015-556. CF was partially supported by NSF grant DMS-1265524, AFOSR grant FA9550-12-1-0425, and Grant No 2014055 from the United States-Israel Binational Science Foundation (BSF).
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Córdoba, D., Fefferman, C. (2016). Water Waves With or Without Surface Tension. In: Giga, Y., Novotny, A. (eds) Handbook of Mathematical Analysis in Mechanics of Viscous Fluids. Springer, Cham. https://doi.org/10.1007/978-3-319-10151-4_30-1
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DOI: https://doi.org/10.1007/978-3-319-10151-4_30-1
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