• Previous Article
    Hölder continuity of solutions to the $A$-Laplace equation involving measures
  • CPAA Home
  • This Issue
  • Next Article
    Cross-constrained variational methods for the nonlinear Klein-Gordon equations with an inverse square potential
September  2009, 8(5): 1555-1575. doi: 10.3934/cpaa.2009.8.1555

Global attractor for the Davey-Stewartson system on $\mathbb R^2$

1. 

Universite de Picardie Jules Verne, LAMFA UMR 7352, 33 rue Saint-Leu, 80039 Amiens cedex

2. 

Laboratoire Paul Painlev, UFR de Mathmatiques Pures et Appliques, Universit des Sciences et Technologies de Lille, 59655 Villeneuve d’Ascq, Equipe SIMPAF INRIA Centre de Recherche Lille Nord Eur, France

Received  August 2008 Revised  January 2009 Published  April 2009

We prove that the weakly damped Davey-Stewartson system (DS), considered as an infinite-dimensional dynamical system in $H^1(\mathbb R^2)$, has a compact global attractor that is actually a compact subset of $H^2(\mathbb R^2)$.
Citation: Olivier Goubet, Manal Hussein. Global attractor for the Davey-Stewartson system on $\mathbb R^2$. Communications on Pure & Applied Analysis, 2009, 8 (5) : 1555-1575. doi: 10.3934/cpaa.2009.8.1555
[1]

Shiming Li, Yongsheng Li, Wei Yan. A global existence and blow-up threshold for Davey-Stewartson equations in $\mathbb{R}^3$. Discrete & Continuous Dynamical Systems - S, 2016, 9 (6) : 1899-1912. doi: 10.3934/dcdss.2016077

[2]

Caroline Obrecht, J.-C. Saut. Remarks on the full dispersion Davey-Stewartson systems. Communications on Pure & Applied Analysis, 2015, 14 (4) : 1547-1561. doi: 10.3934/cpaa.2015.14.1547

[3]

Uchida Hidetake. Analytic smoothing effect and global existence of small solutions for the elliptic-hyperbolic Davey-Stewartson system. Conference Publications, 2001, 2001 (Special) : 182-190. doi: 10.3934/proc.2001.2001.182

[4]

Zaihui Gan, Boling Guo, Jian Zhang. Sharp threshold of global existence for the generalized Davey-Stewartson system in $R^2$. Communications on Pure & Applied Analysis, 2009, 8 (3) : 913-922. doi: 10.3934/cpaa.2009.8.913

[5]

Christian Klein, Benson Muite, Kristelle Roidot. Numerical study of blow-up in the Davey-Stewartson system. Discrete & Continuous Dynamical Systems - B, 2013, 18 (5) : 1361-1387. doi: 10.3934/dcdsb.2013.18.1361

[6]

Jing Lu, Yifei Wu. Sharp threshold for scattering of a generalized Davey-Stewartson system in three dimension. Communications on Pure & Applied Analysis, 2015, 14 (5) : 1641-1670. doi: 10.3934/cpaa.2015.14.1641

[7]

T. Colin, D. Lannes. Justification of and long-wave correction to Davey-Stewartson systems from quadratic hyperbolic systems. Discrete & Continuous Dynamical Systems - A, 2004, 11 (1) : 83-100. doi: 10.3934/dcds.2004.11.83

[8]

Christian Klein, Jean-Claude Saut. A numerical approach to Blow-up issues for Davey-Stewartson II systems. Communications on Pure & Applied Analysis, 2015, 14 (4) : 1443-1467. doi: 10.3934/cpaa.2015.14.1443

[9]

Shitao Liu, Roberto Triggiani. Determining damping and potential coefficients of an inverse problem for a system of two coupled hyperbolic equations. Part I: Global uniqueness. Conference Publications, 2011, 2011 (Special) : 1001-1014. doi: 10.3934/proc.2011.2011.1001

[10]

Eduardo Liz, Gergely Röst. On the global attractor of delay differential equations with unimodal feedback. Discrete & Continuous Dynamical Systems - A, 2009, 24 (4) : 1215-1224. doi: 10.3934/dcds.2009.24.1215

[11]

Hiroshi Matano, Ken-Ichi Nakamura. The global attractor of semilinear parabolic equations on $S^1$. Discrete & Continuous Dynamical Systems - A, 1997, 3 (1) : 1-24. doi: 10.3934/dcds.1997.3.1

[12]

Yuncheng You. Global attractor of the Gray-Scott equations. Communications on Pure & Applied Analysis, 2008, 7 (4) : 947-970. doi: 10.3934/cpaa.2008.7.947

[13]

Ning Ju. The global attractor for the solutions to the 3D viscous primitive equations. Discrete & Continuous Dynamical Systems - A, 2007, 17 (1) : 159-179. doi: 10.3934/dcds.2007.17.159

[14]

Antonio Segatti. Global attractor for a class of doubly nonlinear abstract evolution equations. Discrete & Continuous Dynamical Systems - A, 2006, 14 (4) : 801-820. doi: 10.3934/dcds.2006.14.801

[15]

Ning Ju. The finite dimensional global attractor for the 3D viscous Primitive Equations. Discrete & Continuous Dynamical Systems - A, 2016, 36 (12) : 7001-7020. doi: 10.3934/dcds.2016104

[16]

Francesca Bucci, Igor Chueshov, Irena Lasiecka. Global attractor for a composite system of nonlinear wave and plate equations. Communications on Pure & Applied Analysis, 2007, 6 (1) : 113-140. doi: 10.3934/cpaa.2007.6.113

[17]

Ming Wang. Global attractor for weakly damped gKdV equations in higher sobolev spaces. Discrete & Continuous Dynamical Systems - A, 2015, 35 (8) : 3799-3825. doi: 10.3934/dcds.2015.35.3799

[18]

Wenru Huo, Aimin Huang. The global attractor of the 2d Boussinesq equations with fractional Laplacian in subcritical case. Discrete & Continuous Dynamical Systems - B, 2016, 21 (8) : 2531-2550. doi: 10.3934/dcdsb.2016059

[19]

Ciprian Foias, Ricardo Rosa, Roger Temam. Topological properties of the weak global attractor of the three-dimensional Navier-Stokes equations. Discrete & Continuous Dynamical Systems - A, 2010, 27 (4) : 1611-1631. doi: 10.3934/dcds.2010.27.1611

[20]

Yong Yang, Bingsheng Zhang. On the Kolmogorov entropy of the weak global attractor of 3D Navier-Stokes equations:Ⅰ. Discrete & Continuous Dynamical Systems - B, 2017, 22 (6) : 2339-2350. doi: 10.3934/dcdsb.2017101

2018 Impact Factor: 0.925

Metrics

  • PDF downloads (10)
  • HTML views (0)
  • Cited by (1)

Other articles
by authors

[Back to Top]