On the nonlinear Dysthe equation
Name
2006.13392.pdf
Description
Submitted version
Size
393.62 KB
Format
Adobe PDF
Checksum (MD5)
79b46495cd39efdd772662d51950ada6
Author(s)
Grande, Ricardo
Kurianski, Kristin M
Staffilani, Gigliola
Date Issued
2021
Journal
Nonlinear Analysis, Theory, Methods and Applications
Publisher
Elsevier BV
Version
Original manuscript
Abstract
© 2021 Elsevier Ltd This work is dedicated to putting on a solid analytic ground the theory of local well-posedness for the two dimensional Dysthe equation. This equation can be derived from the incompressible Navier–Stokes equation after performing an asymptotic expansion of a wavetrain modulation to the fourth order. Recently, this equation has been used to numerically study rare phenomena on large water bodies such as rogue waves. In order to study well-posedness, we use Strichartz, and improved smoothing and maximal function estimates. We follow ideas from the pioneering work of Kenig, Ponce and Vega, but since the equation is highly anisotropic, several technical challenges had to be resolved. We conclude our work by also presenting an ill-posedness result.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
Creative Commons Attribution-NonCommercial-NoDerivs License
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1016/j.na.2021.112292
