Long Wave Approximations for Water Waves

By Jerry L. Bona, Thierry Colin, David Lannes. 2005

312 citations recorded by the source corpus.

Subfields: Applied Mathematics, Earth-Surface Processes, Oceanography

View Paper: https://www.semanticscholar.org/paper/b6b9389d09a227f6cc09bd9e44d0885b9df75ded

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In Applied Mathematics

In Earth-Surface Processes

In Oceanography

Citations in the corpus

The Cauchy problem on large time for surface waves Boussinesq systems (2012, methodology): “Starting from the incompressible Euler equations with free surface, assuming that the flow is potential, the bottom is flat and neglecting surface tension, one derives in this regime a family of asymptotic models [5,7].”
Nonhomogeneous Boundary-Value Problems for One-Dimensional Nonlinear Schr\"odinger Equations (2015, methodology): “Justifying the simpler model as an approximation of a more elaborate model typically requires smoothness of the solutions of both the full and the approximate models (see [5, 34, 66] for justification of the KdV equation as an approximation of the full water-wave problem, for instance).”
Well-posedness of the water-waves equations (2005, methodology): “Choosing the most simple diffeomorphism between the fluid domain and S as in [12, 2 ] and applying Theorem 2.9 to the elliptic problem thus obtained, we can obtain, via Prop.”
Large time existence for 3D water-waves and asymptotics (2007, methodology): “This method has been used in the long-waves regime in [5,32,9] (see also [39]) where the corresponding expansions of the DN operator can be found.”
Boussinesq equations and other systems for small-amplitude long waves in nonlinear dispersive media: II. The nonlinear theory (2004, background): “If nonlinear changes are countenanced, larger classes of formally correct approximations emerge (see [6, 12]).”
Asymptotic Models for Internal Waves (2007, methodology): “The same remark has already been made about the Boussinesq systems for wave propagation in the case of surface gravity waves [8, 10]).”
Solitary water wave interactions (2006, methodology): “For more precise estimates we cite Bona, Colin, and Lannes 22 and Wright, 23 the latter giving the currently best rigorous result on the higher-order correction terms.”