# American Institute of Mathematical Sciences

August  2015, 35(8): 3799-3825. doi: 10.3934/dcds.2015.35.3799

## Global attractor for weakly damped gKdV equations in higher sobolev spaces

 1 School of Mathematics and Physics, China University of Geosciences, Wuhan, 430074, China

Received  August 2014 Revised  December 2014 Published  February 2015

Long time behavior of solutions for weakly damped gKdV equations on the real line is studied. With some weak regularity assumptions on the force $f$, we prove the existence of global attractor in $H^s$ for any $s\geq 1$. The asymptotic compactness of solution semigroup is shown by Ball's energy method and Goubet's high-low frequency decomposition if $s$ is an integer and not an integer, respectively.
Citation: Ming Wang. Global attractor for weakly damped gKdV equations in higher sobolev spaces. Discrete & Continuous Dynamical Systems, 2015, 35 (8) : 3799-3825. doi: 10.3934/dcds.2015.35.3799
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