
Previous Article
The existence of a global attractor for a KuramotoSivashinsky 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, UAMAzc., Av. San Pablo 180, Col. Reynosa, México D. F. 02200, Mexico 
2.  San Antonio 64, Col. Las Fuentes, Zapopan, Jalisco, 45070, Mexico 
$V$ 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 ${Cr}=\{\omega\in S^{n1}:\nabla V(\omega)=0\}$, $n\geq 3$, 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 zeroenergy 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] 
Zhengan Yao, YuLong Zhou. High order approximation for the Boltzmann equation without angular cutoff under moderately soft potentials. Kinetic & Related Models, 2020, 13 (3) : 435478. 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 & Related Models, 2019, 12 (3) : 483505. doi: 10.3934/krm.2019020 
[3] 
Henryk Leszczyński, Monika Wrzosek. Newton's method for nonlinear stochastic wave equations driven by onedimensional Brownian motion. Mathematical Biosciences & Engineering, 2017, 14 (1) : 237248. doi: 10.3934/mbe.2017015 
[4] 
Koichi Osaki, Hirotoshi Satoh, Shigetoshi Yazaki. Towards modelling spiral motion of open plane curves. Discrete & Continuous Dynamical Systems  S, 2015, 8 (5) : 10091022. 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 & Applied Analysis, 2014, 13 (5) : 16851718. doi: 10.3934/cpaa.2014.13.1685 
[6] 
Tetsuya Ishiwata. Crystalline motion of spiralshaped polygonal curves with a tip motion. Discrete & Continuous Dynamical Systems  S, 2014, 7 (1) : 5362. doi: 10.3934/dcdss.2014.7.53 
[7] 
Tetsuya Ishiwata. On spiral solutions to generalized crystalline motion with a rotating tip motion. Discrete & Continuous Dynamical Systems  S, 2015, 8 (5) : 881888. doi: 10.3934/dcdss.2015.8.881 
[8] 
Renjun Duan, Shuangqian Liu, Tong Yang, Huijiang Zhao. Stability of the nonrelativistic VlasovMaxwellBoltzmann system for angular noncutoff potentials. Kinetic & Related Models, 2013, 6 (1) : 159204. 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 & Related Models, 2008, 1 (3) : 453489. doi: 10.3934/krm.2008.1.453 
[10] 
Yoshinori Morimoto, Seiji Ukai, ChaoJiang Xu, Tong Yang. Regularity of solutions to the spatially homogeneous Boltzmann equation without angular cutoff. Discrete & Continuous Dynamical Systems  A, 2009, 24 (1) : 187212. doi: 10.3934/dcds.2009.24.187 
[11] 
Lingbing He, Yulong Zhou. High order approximation for the Boltzmann equation without angular cutoff. Kinetic & Related Models, 2018, 11 (3) : 547596. doi: 10.3934/krm.2018024 
[12] 
Hideo Ikeda, Koji Kondo, Hisashi Okamoto, Shoji Yotsutani. On the global branches of the solutions to a nonlocal boundaryvalue problem arising in Oseen's spiral flows. Communications on Pure & Applied Analysis, 2003, 2 (3) : 381390. 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) : 294303. doi: 10.3934/proc.2007.2007.294 
[14] 
Juhi Jang, Ian Tice. Passive scalars, moving boundaries, and Newton's law of cooling. Discrete & Continuous Dynamical Systems  A, 2016, 36 (3) : 13831413. doi: 10.3934/dcds.2016.36.1383 
[15] 
R. Baier, M. Dellnitz, M. Hesselvon Molo, S. Sertl, I. G. Kevrekidis. The computation of convex invariant sets via Newton's method. Journal of Computational Dynamics, 2014, 1 (1) : 3969. 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 & Management Optimization, 2008, 4 (1) : 143153. doi: 10.3934/jimo.2008.4.143 
[17] 
Xavier Blanc, Claude Le Bris, PierreLouis Lions. From the Newton equation to the wave equation in some simple cases. Networks & Heterogeneous Media, 2012, 7 (1) : 141. doi: 10.3934/nhm.2012.7.1 
[18] 
Basim A. Hassan. A new type of quasinewton updating formulas based on the new quasinewton equation. Numerical Algebra, Control & Optimization, 2020, 10 (2) : 227235. 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) : 461485. doi: 10.3934/jgm.2016016 
[20] 
Letizia Stefanelli, Ugo Locatelli. Kolmogorov's normal form for equations of motion with dissipative effects. Discrete & Continuous Dynamical Systems  B, 2012, 17 (7) : 25612593. doi: 10.3934/dcdsb.2012.17.2561 
Impact Factor:
Tools
Metrics
Other articles
by authors
[Back to Top]