[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 …
the NSF-CBMS international research conference organized at the Mathematics Department …
Global bifurcation of steady gravity water waves with critical layers
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 …
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 …
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 …
constant vorticity over a flat bed. Using conformal mappings the free-boundary problem is …
Traveling water waves—the ebb and flow of two centuries
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 …
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 …
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 …
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,∞ …
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 …
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 …
peaked soliton for an integrable modified Camassa-Holm equation with cubic nonlinearity …