-
Previous Article
The existence of a global attractor for a Kuramoto-Sivashinsky type equation in 2D
- PROC Home
- This Issue
-
Next Article
Comparison among different notions of solution for the $p$-system at a junction
Spiral motion in classical mechanics
| 1. | Departamento de Ciencias Básicas, UAM-Azc., Av. San Pablo 180, Col. Reynosa, México D. F. 02200, Mexico |
| 2. | San Antonio 64, Col. Las Fuentes, Zapopan, Jalisco, 45070, Mexico |
- Abstract
- Related Papers
Under a Creative Commons license
$V$ in dimension three, which exhibits an orbit that spirals as time goes to infinity. This kind of orbits cannot occur for this class of potentials in dimension two [4] or, see below, if ${Cr}=\{\omega\in S^{n-1}:\nabla V(\omega)=0\}$, $n\geq 3$, is totally disconnected. In addition, for each $\mu>2$ we give an example of a potential of the form $V(r,\theta)=O(r^{-\mu})$, in two dimensions, which is not radially symmetric and has a zero-energy orbit that escapes towards infinity in spirals. Zero energy orbits escaping towards infinity in spirals cannot occur for radial potentials with the same rate of decay.
| [1] |
Zheng-an Yao, Yu-Long Zhou. High order approximation for the Boltzmann equation without angular cutoff under moderately soft potentials. Kinetic and Related Models, 2020, 13 (3) : 435-478. doi: 10.3934/krm.2020015 |
| [2] |
Nicolas Fournier. A recursive algorithm and a series expansion related to the homogeneous Boltzmann equation for hard potentials with angular cutoff. Kinetic and Related Models, 2019, 12 (3) : 483-505. doi: 10.3934/krm.2019020 |
| [3] |
Henryk Leszczyński, Monika Wrzosek. Newton's method for nonlinear stochastic wave equations driven by one-dimensional Brownian motion. Mathematical Biosciences & Engineering, 2017, 14 (1) : 237-248. doi: 10.3934/mbe.2017015 |
| [4] |
Koichi Osaki, Hirotoshi Satoh, Shigetoshi Yazaki. Towards modelling spiral motion of open plane curves. Discrete and Continuous Dynamical Systems - S, 2015, 8 (5) : 1009-1022. doi: 10.3934/dcdss.2015.8.1009 |
| [5] |
Anatoli Babin, Alexander Figotin. Newton's law for a trajectory of concentration of solutions to nonlinear Schrodinger equation. Communications on Pure and Applied Analysis, 2014, 13 (5) : 1685-1718. doi: 10.3934/cpaa.2014.13.1685 |
| [6] |
Tetsuya Ishiwata. Crystalline motion of spiral-shaped polygonal curves with a tip motion. Discrete and Continuous Dynamical Systems - S, 2014, 7 (1) : 53-62. doi: 10.3934/dcdss.2014.7.53 |
| [7] |
Tetsuya Ishiwata. On spiral solutions to generalized crystalline motion with a rotating tip motion. Discrete and Continuous Dynamical Systems - S, 2015, 8 (5) : 881-888. doi: 10.3934/dcdss.2015.8.881 |
| [8] |
Renjun Duan, Shuangqian Liu, Tong Yang, Huijiang Zhao. Stability of the nonrelativistic Vlasov-Maxwell-Boltzmann system for angular non-cutoff potentials. Kinetic and Related Models, 2013, 6 (1) : 159-204. doi: 10.3934/krm.2013.6.159 |
| [9] |
Zhaohui Huo, Yoshinori Morimoto, Seiji Ukai, Tong Yang. Regularity of solutions for spatially homogeneous Boltzmann equation without angular cutoff. Kinetic and Related Models, 2008, 1 (3) : 453-489. doi: 10.3934/krm.2008.1.453 |
| [10] |
Lingbing He, Yulong Zhou. High order approximation for the Boltzmann equation without angular cutoff. Kinetic and Related Models, 2018, 11 (3) : 547-596. doi: 10.3934/krm.2018024 |
| [11] |
Yoshinori Morimoto, Seiji Ukai, Chao-Jiang Xu, Tong Yang. Regularity of solutions to the spatially homogeneous Boltzmann equation without angular cutoff. Discrete and Continuous Dynamical Systems, 2009, 24 (1) : 187-212. doi: 10.3934/dcds.2009.24.187 |
| [12] |
Hideo Ikeda, Koji Kondo, Hisashi Okamoto, Shoji Yotsutani. On the global branches of the solutions to a nonlocal boundary-value problem arising in Oseen's spiral flows. Communications on Pure and Applied Analysis, 2003, 2 (3) : 381-390. doi: 10.3934/cpaa.2003.2.381 |
| [13] |
Robert Denk, Leonid Volevich. A new class of parabolic problems connected with Newton's polygon. Conference Publications, 2007, 2007 (Special) : 294-303. doi: 10.3934/proc.2007.2007.294 |
| [14] |
Juhi Jang, Ian Tice. Passive scalars, moving boundaries, and Newton's law of cooling. Discrete and Continuous Dynamical Systems, 2016, 36 (3) : 1383-1413. doi: 10.3934/dcds.2016.36.1383 |
| [15] |
R. Baier, M. Dellnitz, M. Hessel-von Molo, S. Sertl, I. G. Kevrekidis. The computation of convex invariant sets via Newton's method. Journal of Computational Dynamics, 2014, 1 (1) : 39-69. doi: 10.3934/jcd.2014.1.39 |
| [16] |
Liqun Qi, Zheng yan, Hongxia Yin. Semismooth reformulation and Newton's method for the security region problem of power systems. Journal of Industrial and Management Optimization, 2008, 4 (1) : 143-153. doi: 10.3934/jimo.2008.4.143 |
| [17] |
Xavier Blanc, Claude Le Bris, Pierre-Louis Lions. From the Newton equation to the wave equation in some simple cases. Networks and Heterogeneous Media, 2012, 7 (1) : 1-41. doi: 10.3934/nhm.2012.7.1 |
| [18] |
Basim A. Hassan. A new type of quasi-newton updating formulas based on the new quasi-newton equation. Numerical Algebra, Control and Optimization, 2020, 10 (2) : 227-235. doi: 10.3934/naco.2019049 |
| [19] |
Banavara N. Shashikanth. Kirchhoff's equations of motion via a constrained Zakharov system. Journal of Geometric Mechanics, 2016, 8 (4) : 461-485. doi: 10.3934/jgm.2016016 |
| [20] |
Letizia Stefanelli, Ugo Locatelli. Kolmogorov's normal form for equations of motion with dissipative effects. Discrete and Continuous Dynamical Systems - B, 2012, 17 (7) : 2561-2593. doi: 10.3934/dcdsb.2012.17.2561 |
Impact Factor:
Tools
Metrics
Other articles
by authors
[Back to Top]