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Sufficient conditions for the regularity to the 3D Navier-Stokes equations
Solitary-wave solutions to Boussinesq systems with large surface tension
| 1. | Department of Mathematics, Purdue University, West Lafayette, IN 47907 |
| 2. | Department of Mathematics and Statistics, Utah State University, Logan, UT 84322, United States |
| 3. | Department of Mathematics, Virginia Tech, Blacksburg, VA 24061 |
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Mathias Nikolai Arnesen. Existence of solitary-wave solutions to nonlocal equations. Discrete and Continuous Dynamical Systems, 2016, 36 (7) : 3483-3510. doi: 10.3934/dcds.2016.36.3483 |
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Y. A. Li, P. J. Olver. Convergence of solitary-wave solutions in a perturbed bi-Hamiltonian dynamical system I. Compactions and peakons. Discrete and Continuous Dynamical Systems, 1997, 3 (3) : 419-432. doi: 10.3934/dcds.1997.3.419 |
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Jerry L. Bona, Didier Pilod. Stability of solitary-wave solutions to the Hirota-Satsuma equation. Discrete and Continuous Dynamical Systems, 2010, 27 (4) : 1391-1413. doi: 10.3934/dcds.2010.27.1391 |
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Y. A. Li, P. J. Olver. Convergence of solitary-wave solutions in a perturbed bi-hamiltonian dynamical system ii. complex analytic behavior and convergence to non-analytic solutions. Discrete and Continuous Dynamical Systems, 1998, 4 (1) : 159-191. doi: 10.3934/dcds.1998.4.159 |
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Jerry L. Bona, Angel Durán, Dimitrios Mitsotakis. Solitary-wave solutions of Benjamin-Ono and other systems for internal waves. I. approximations. Discrete and Continuous Dynamical Systems, 2021, 41 (1) : 87-111. doi: 10.3934/dcds.2020215 |
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Shengfu Deng. Generalized multi-hump wave solutions of Kdv-Kdv system of Boussinesq equations. Discrete and Continuous Dynamical Systems, 2019, 39 (7) : 3671-3716. doi: 10.3934/dcds.2019150 |
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Jibin Li, Yi Zhang. Exact solitary wave and quasi-periodic wave solutions for four fifth-order nonlinear wave equations. Discrete and Continuous Dynamical Systems - B, 2010, 13 (3) : 623-631. doi: 10.3934/dcdsb.2010.13.623 |
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Jibin Li. Family of nonlinear wave equations which yield loop solutions and solitary wave solutions. Discrete and Continuous Dynamical Systems, 2009, 24 (3) : 897-907. doi: 10.3934/dcds.2009.24.897 |
| [9] |
Radosław Kurek, Paweł Lubowiecki, Henryk Żołądek. The Hess-Appelrot system. Ⅲ. Splitting of separatrices and chaos. Discrete and Continuous Dynamical Systems, 2018, 38 (4) : 1955-1981. doi: 10.3934/dcds.2018079 |
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José Raúl Quintero, Juan Carlos Muñoz Grajales. Solitary waves for an internal wave model. Discrete and Continuous Dynamical Systems, 2016, 36 (10) : 5721-5741. doi: 10.3934/dcds.2016051 |
| [11] |
Rui Liu. Several new types of solitary wave solutions for the generalized Camassa-Holm-Degasperis-Procesi equation. Communications on Pure and Applied Analysis, 2010, 9 (1) : 77-90. doi: 10.3934/cpaa.2010.9.77 |
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Xiaowan Li, Zengji Du, Shuguan Ji. Existence results of solitary wave solutions for a delayed Camassa-Holm-KP equation. Communications on Pure and Applied Analysis, 2019, 18 (6) : 2961-2981. doi: 10.3934/cpaa.2019132 |
| [13] |
Karine Adamy. Existence of solutions for a Boussinesq system on the half line and on a finite interval. Discrete and Continuous Dynamical Systems, 2011, 29 (1) : 25-49. doi: 10.3934/dcds.2011.29.25 |
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George J. Bautista, Ademir F. Pazoto. Decay of solutions for a dissipative higher-order Boussinesq system on a periodic domain. Communications on Pure and Applied Analysis, 2020, 19 (2) : 747-769. doi: 10.3934/cpaa.2020035 |
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Yuming Qin, Yang Wang, Xing Su, Jianlin Zhang. Global existence of solutions for the three-dimensional Boussinesq system with anisotropic data. Discrete and Continuous Dynamical Systems, 2016, 36 (3) : 1563-1581. doi: 10.3934/dcds.2016.36.1563 |
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Sevdzhan Hakkaev. Orbital stability of solitary waves of the Schrödinger-Boussinesq equation. Communications on Pure and Applied Analysis, 2007, 6 (4) : 1043-1050. doi: 10.3934/cpaa.2007.6.1043 |
| [17] |
Zongyuan Li, Weinan Wang. Norm inflation for the Boussinesq system. Discrete and Continuous Dynamical Systems - B, 2021, 26 (10) : 5449-5463. doi: 10.3934/dcdsb.2020353 |
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Sébastien Court. Stabilization of a fluid-solid system, by the deformation of the self-propelled solid. Part II: The nonlinear system.. Evolution Equations and Control Theory, 2014, 3 (1) : 83-118. doi: 10.3934/eect.2014.3.83 |
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Sébastien Court. Stabilization of a fluid-solid system, by the deformation of the self-propelled solid. Part I: The linearized system.. Evolution Equations and Control Theory, 2014, 3 (1) : 59-82. doi: 10.3934/eect.2014.3.59 |
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Paweł Lubowiecki, Henryk Żołądek. The Hess-Appelrot system. I. Invariant torus and its normal hyperbolicity. Journal of Geometric Mechanics, 2012, 4 (4) : 443-467. doi: 10.3934/jgm.2012.4.443 |
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