Starting from the paper by Dias, Dyachenko, and Zakharov (Physics Letters A, 2008) on viscous water waves, we derive a model that describes water waves with viscosity moving in deep water with or without surface tension effects. This equation takes the form of a nonlocal fourth order wave equation and retains the main contributions to the dynamics of the free surface. Then, we prove the well-posedness in Sobolev spaces of such an equation.
Well-posedness of water wave model with viscous effects / Granero-Belinchon, R; Scrobogna, S. - In: PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY. - ISSN 0002-9939. - 148/2020:12(2020), pp. 5181-5191. [10.1090/proc/15219]
Well-posedness of water wave model with viscous effects
Scrobogna S
2020-01-01
Abstract
Starting from the paper by Dias, Dyachenko, and Zakharov (Physics Letters A, 2008) on viscous water waves, we derive a model that describes water waves with viscosity moving in deep water with or without surface tension effects. This equation takes the form of a nonlocal fourth order wave equation and retains the main contributions to the dynamics of the free surface. Then, we prove the well-posedness in Sobolev spaces of such an equation.| File | Dimensione | Formato | |
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