American Institute of Mathematical Sciences

Bashar Khorbatly. Long, intermediate and short-term well-posedness of high precision shallow-water models with topography variations. Discrete and Continuous Dynamical Systems - B, 2022  doi: 10.3934/dcdsb.2022068

Robert McOwen, Peter Topalov. Asymptotics in shallow water waves. Discrete and Continuous Dynamical Systems, 2015, 35 (7) : 3103-3131. doi: 10.3934/dcds.2015.35.3103

Vincent Duchêne, Samer Israwi, Raafat Talhouk. Shallow water asymptotic models for the propagation of internal waves. Discrete and Continuous Dynamical Systems - S, 2014, 7 (2) : 239-269. doi: 10.3934/dcdss.2014.7.239

Bilal Al Taki, Khawla Msheik, Jacques Sainte-Marie. On the rigid-lid approximation of shallow water Bingham. Discrete and Continuous Dynamical Systems - B, 2021, 26 (2) : 875-905. doi: 10.3934/dcdsb.2020146

Julien Chambarel, Christian Kharif, Olivier Kimmoun. Focusing wave group in shallow water in the presence of wind. Discrete and Continuous Dynamical Systems - B, 2010, 13 (4) : 773-782. doi: 10.3934/dcdsb.2010.13.773

Anna Geyer, Ronald Quirchmayr. Shallow water models for stratified equatorial flows. Discrete and Continuous Dynamical Systems, 2019, 39 (8) : 4533-4545. doi: 10.3934/dcds.2019186

Madalina Petcu, Roger Temam. The one dimensional shallow water equations with Dirichlet boundary conditions on the velocity. Discrete and Continuous Dynamical Systems - S, 2011, 4 (1) : 209-222. doi: 10.3934/dcdss.2011.4.209

Zhigang Wang. Vanishing viscosity limit of the rotating shallow water equations with far field vacuum. Discrete and Continuous Dynamical Systems, 2018, 38 (1) : 311-328. doi: 10.3934/dcds.2018015

Chengchun Hao. Cauchy problem for viscous shallow water equations with surface tension. Discrete and Continuous Dynamical Systems - B, 2010, 13 (3) : 593-608. doi: 10.3934/dcdsb.2010.13.593

Issam S. Strub, Julie Percelay, Olli-Pekka Tossavainen, Alexandre M. Bayen. Comparison of two data assimilation algorithms for shallow water flows. Networks and Heterogeneous Media, 2009, 4 (2) : 409-430. doi: 10.3934/nhm.2009.4.409

Olivier Delestre, Arthur R. Ghigo, José-Maria Fullana, Pierre-Yves Lagrée. A shallow water with variable pressure model for blood flow simulation. Networks and Heterogeneous Media, 2016, 11 (1) : 69-87. doi: 10.3934/nhm.2016.11.69

Denys Dutykh, Dimitrios Mitsotakis. On the relevance of the dam break problem in the context of nonlinear shallow water equations. Discrete and Continuous Dynamical Systems - B, 2010, 13 (4) : 799-818. doi: 10.3934/dcdsb.2010.13.799

Nora Aïssiouene, Marie-Odile Bristeau, Edwige Godlewski, Jacques Sainte-Marie. A combined finite volume - finite element scheme for a dispersive shallow water system. Networks and Heterogeneous Media, 2016, 11 (1) : 1-27. doi: 10.3934/nhm.2016.11.1

Werner Bauer, François Gay-Balmaz. Towards a geometric variational discretization of compressible fluids: The rotating shallow water equations. Journal of Computational Dynamics, 2019, 6 (1) : 1-37. doi: 10.3934/jcd.2019001

Roberto Camassa. Characteristics and the initial value problem of a completely integrable shallow water equation. Discrete and Continuous Dynamical Systems - B, 2003, 3 (1) : 115-139. doi: 10.3934/dcdsb.2003.3.115

Daniel Guo, John Drake. A global semi-Lagrangian spectral model for the reformulated shallow water equations. Conference Publications, 2003, 2003 (Special) : 375-385. doi: 10.3934/proc.2003.2003.375

Xiaoping Zhai, Hailong Ye. On global large energy solutions to the viscous shallow water equations. Discrete and Continuous Dynamical Systems - B, 2020, 25 (11) : 4277-4293. doi: 10.3934/dcdsb.2020097

Madalina Petcu, Roger Temam. An interface problem: The two-layer shallow water equations. Discrete and Continuous Dynamical Systems, 2013, 33 (11&12) : 5327-5345. doi: 10.3934/dcds.2013.33.5327

Mouhamadou Aliou M. T. Baldé, Diaraf Seck. Coupling the shallow water equation with a long term dynamics of sand dunes. Discrete and Continuous Dynamical Systems - S, 2016, 9 (5) : 1521-1551. doi: 10.3934/dcdss.2016061

Marcel Oliver, Sergiy Vasylkevych. Hamiltonian formalism for models of rotating shallow water in semigeostrophic scaling. Discrete and Continuous Dynamical Systems, 2011, 31 (3) : 827-846. doi: 10.3934/dcds.2011.31.827