The attractor for the two-dimensional weakly damped KdV equation in belt field

DOI10.1016/j.nonrwa.2007.01.009zbMath1147.35089OpenAlexW2065042448MaRDI QIDQ933557

Lixin Tian, Ruihua Tian

Publication date: 21 July 2008

Published in: Nonlinear Analysis. Real World Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.nonrwa.2007.01.009

zbMATH Keywords

global attractorenergy equationBourgain spacebelt fieldtwo-dimensional weakly damped KdV equation

Mathematics Subject Classification ID

Attractors (35B41) KdV equations (Korteweg-de Vries equations) (35Q53) Attractors and their dimensions, Lyapunov exponents for infinite-dimensional dissipative dynamical systems (37L30)

Related Items (6)

The global attractor for a viscous weakly dissipative generalized two-component \(\mu\)-Hunter-Saxton system ⋮ Attractor for a viscous coupled Camassa-Holm equation ⋮ Low-regularity solutions of the periodic general Degasperis-Procesi equation ⋮ The global attractor of the viscous Fornberg-Whitham equation ⋮ The global attractor and numerical simulation of a forced weakly damped MKdV equation ⋮ The global attractor of the viscous damped forced Ostrovsky equation

Cites Work

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• Existence and finite dimensionality of the global attractor for evolution equations on unbounded domains
• Weakly damped forced Korteweg-de Vries equations behave as a finite dimensional dynamical system in the long time
• Fourier transform restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations. II: The KdV-equation
• The Cauchy problem for the Korteweg-de Vries equation in Sobolev spaces of negative indices
• A note on the strong convergence towards attractors of damped forced KdV equations
• Attractors of dissipative soliton equation
• Wavelet approximate inertial manifold and numerical solution of Burgers' equation
• On the regularity of the global attractor of a weakly damped, forced Korteweg-de Vries equation
• Asymptotic smoothing and the global attractor of a weakly damped KdV equation on the real line.
• Global attractors for the three-dimensional Navier-Stokes equations
• The study on solutions to Camassa-Holm equation with weak dissipation
• On the well-posedness problem and the scattering problem for the Dullin-Gottwald-Holm equation
• Well-Posedness of the Initial Value Problem for the Korteweg-de Vries Equation
• Attractors for non-compact semigroups via energy equations
• Compact attractor for weakly damped driven Korteweg-de Vries equations on the real line
• A bilinear estimate with applications to the KdV equation

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