[图书][B] Nonlinear water waves with applications to wave-current interactions and tsunamis

A Constantin - 2011 - SIAM
This book is the written and somewhat expanded version of the author's lectures delivered at
the NSF-CBMS international research conference organized at the Mathematics Department …

Global bifurcation of steady gravity water waves with critical layers

A Constantin, W Strauss, E Vărvărucă - 2016 - projecteuclid.org
We construct families of two-dimensional travelling water waves propagating under the
influence of gravity in a flow of constant vorticity over a flat bed, in particular establishing the …

Soliton resolution and large time behavior of solutions to the Cauchy problem for the Novikov equation with a nonzero background

Y Yang, E Fan - Advances in Mathematics, 2023 - Elsevier
In this paper, we study the soliton resolution and large time behavior of solutions to the
Cauchy problem for the Novikov equation with a nonzero background ut− utx x+ 4 ux= 3 …

Steady periodic water waves with constant vorticity: regularity and local bifurcation

A Constantin, E Varvaruca - Archive for rational mechanics and analysis, 2011 - Springer
This paper studies periodic traveling gravity waves at the free surface of water in a flow of
constant vorticity over a flat bed. Using conformal mappings the free-boundary problem is …

Traveling water waves—the ebb and flow of two centuries

S Haziot, V Hur, W Strauss, J Toland, E Wahlén… - Quarterly of applied …, 2022 - ams.org
This survey covers the mathematical theory of steady water waves with an emphasis on
topics that are at the forefront of current research. These areas include: variational …

[HTML][HTML] Remarks on the well-posedness of Camassa–Holm type equations in Besov spaces

J Li, Z Yin - Journal of Differential Equations, 2016 - Elsevier
In this paper, we prove the solution map of the Cauchy problem of Camassa–Holm type
equations depends continuously on the initial data in nonhomogeneous Besov spaces in …

[HTML][HTML] Non-uniform dependence on initial data for the Camassa-Holm equation in Besov spaces

J Li, Y Yu, W Zhu - Journal of Differential Equations, 2020 - Elsevier
In the paper, we consider the initial value problem to the Camassa-Holm equation in the real-
line case. Based on the local well-posedness result and the lifespan, we proved that the …

Ill-posedness for the Camassa-Holm and related equations in Besov spaces

J Li, Y Yu, W Zhu - Journal of Differential Equations, 2022 - Elsevier
In this paper, we give a construction of u 0∈ B p,∞ σ such that the corresponding solution to
the Camassa-Holm equation starting from u 0 is discontinuous at t= 0 in the metric of B p,∞ …

Capturing the flow beneath water waves

A Nachbin, R Ribeiro-Junior - … Transactions of the …, 2018 - royalsocietypublishing.org
Recently, the authors presented two numerical studies for capturing the flow structure
beneath water waves (Nachbin and Ribeiro-Junior 2014 Disc. Cont. Dyn. Syst. A 34, 3135 …

Stability of peakons for an integrable modified Camassa-Holm equation with cubic nonlinearity

C Qu, X Liu, Y Liu - Communications in Mathematical Physics, 2013 - Springer
Considered herein is the dynamical stability of the single peaked soliton and periodic
peaked soliton for an integrable modified Camassa-Holm equation with cubic nonlinearity …