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The Lifespan of Small Data Solutions in Two Dimensional Capillary Water Waves

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Abstract

This article is concerned with the incompressible, irrotational infinite depth water wave equation in two space dimensions, without gravity but with surface tension. We consider this problem expressed in position–velocity potential holomorphic coordinates, and prove that small data solutions have at least cubic lifespan while small localized data leads to global solutions.

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Authors and Affiliations

  1. Department of Mathematics, University of California at Berkeley, Berkeley, CA, USA

    Mihaela Ifrim & Daniel Tataru

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  1. Mihaela Ifrim
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  2. Daniel Tataru
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Correspondence to Daniel Tataru.

Additional information

Communicated by V. Šverák

The first author was supported by the Simons Foundation.

The second author was partially supported by the NSF Grant DMS-1266182 as well as by the Simons Foundation.

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Ifrim, M., Tataru, D. The Lifespan of Small Data Solutions in Two Dimensional Capillary Water Waves. Arch Rational Mech Anal 225, 1279–1346 (2017). https://doi.org/10.1007/s00205-017-1126-z

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  • DOI: https://doi.org/10.1007/s00205-017-1126-z

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