Spatially Quasi-Periodic Solutions of the Euler Equation

被引：1
|
作者：
Sun, Xu [1 ]
Topalov, Peter [1 ]
机构：
[1] Northeastern Univ, Dept Math, Boston, MA 02115 USA
来源：
JOURNAL OF MATHEMATICAL FLUID MECHANICS | 2023年 / 25卷 / 03期
关键词：
QUASIPATTERNS; EXISTENCE; DIFFEOMORPHISMS;
D O I：
10.1007/s00021-023-00804-9
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We develop a framework for studying quasi-periodic maps and diffeomorphisms on R-n. As an application, we prove that the Euler equation is locally well posed in a space of quasi-periodic vector fields on R-n. In particular, the equation preserves the spatial quasi-periodicity of the initial data. Several results on the analytic dependence of solutions on the time and the initial data are proved.
引用
收藏
页数：34
相关论文
共 50 条
  • [1] Spatially Quasi-Periodic Solutions of the Euler Equation
    Xu Sun
    Peter Topalov
    [J]. Journal of Mathematical Fluid Mechanics, 2023, 25
  • [2] Quasi-periodic solutions of the 2D Euler equation
    Crouseilles, Nicolas
    Faou, Erwan
    [J]. ASYMPTOTIC ANALYSIS, 2013, 81 (01) : 31 - 34
  • [3] THE CONSTRUCTION OF QUASI-PERIODIC SOLUTIONS OF QUASI-PERIODIC FORCED SCHRODINGER EQUATION
    Jiao, Lei
    Wang, Yiqian
    [J]. COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, 2009, 8 (05) : 1585 - 1606
  • [4] QUASI-PERIODIC SOLUTIONS OF GENERALIZED BOUSSINESQ EQUATION WITH QUASI-PERIODIC FORCING
    Shi, Yanling
    Xu, Junxiang
    Xu, Xindong
    [J]. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, 2017, 22 (06): : 2501 - 2519
  • [5] QUASI-PERIODIC SOLUTIONS OF THE BOOMERON EQUATION
    MARTINI, R
    WESSELIUS, W
    [J]. JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 1985, 18 (09): : 1315 - 1326
  • [6] Local existence and uniqueness of spatially quasi-periodic solutions to the generalized KdV equation
    Damanik, David
    Li, Yong
    Xu, Fei
    [J]. JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES, 2024, 186 : 251 - 302
  • [7] Quasi-periodic Solutions for a Class of Higher Dimensional Beam Equation with Quasi-periodic Forcing
    Yanling Shi
    Junxiang Xu
    Xindong Xu
    [J]. Journal of Dynamics and Differential Equations, 2019, 31 : 745 - 763
  • [8] Quasi-periodic Solutions for a Class of Higher Dimensional Beam Equation with Quasi-periodic Forcing
    Shi, Yanling
    Xu, Junxiang
    Xu, Xindong
    [J]. JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS, 2019, 31 (02) : 745 - 763
  • [9] Quasi-Periodic Solutions and Stability for a Weakly Damped Nonlinear Quasi-Periodic Mathieu Equation
    K. Guennoun
    M. Houssni
    M. Belhaq
    [J]. Nonlinear Dynamics, 2002, 27 : 211 - 236
  • [10] A result on quasi-periodic solutions of a nonlinear beam equation with a quasi-periodic forcing term
    Yi Wang
    Jianguo Si
    [J]. Zeitschrift für angewandte Mathematik und Physik, 2012, 63 : 189 - 190
12345